Arteta, 37, became the first confirmed member of staff of a Premier League team to contract the disease, which was officially labelled a pandemic by the World Health Organisation on Wednesday.
News of Arteta’s diagnosis came less than an hour after the Premier League announced that this weekend’s fixtures would still be played as planned.
He, and the entire first-team squad and coaching staff, will now be self-isolating in accordance with the most recent government guidelines.
Chelsea announced Hudson-Odoi, 19, had tested positive with COVID-19 at around midnight and said the training facility in Cobham, Surrey, will be partially closed.
Chelsea staff who had recent close contact with the winger will also self-isolate, the club said in a statement.
The Premier League will hold an emergency meeting via conference call at 10.30am on Friday to decide if and how to proceed with the remaining fixtures of the season.
Earlier today Prime Minister Boris Johnson chaired a meeting of Cobra emergency committee in which he refused to ban mass gatherings or shut schools despite saying ‘many loved ones’ will die during the escalating crisis.
Arsenal were due to play Brighton on Saturday, but the South Coast club announced this evening that the match is postponed.
It is understood Arteta did not come into contact with Olympiakos owner Evangelos Marinakis, who also tested positive, during their Europa League game on February 27.
There are over 590 confirmed cases of the virus in the UK, and 10 people have died from it so far. Nearly 5,000 people have died worldwide, and the number of cases has shot up to over 130,000.
The prime minister today branded the virus the ‘worst public health crisis in a generation’ and warned that ‘many more’ people are going to die, but still held off drastic measures.
At a press conference in Westminster, Mr Johnson formally declared that the UK’s tactics have shifted from ‘containing’ the killer disease to merely ‘delaying’ its inevitable spread, after he chaired a meeting of the Cobra emergency committee.
Mr Johnson said it was clear the disease will continue to spread around the world and people should brace for the ‘reality’ of ‘severe disruption’ for many months.
The Government’s new plan urges anyone with even mild coronavirus-like symptoms – a persistent cough or a fever – to quarantine themselves at home and to sleep alone if possible and stay at least two metres from relatives.
The PM has also recommended all overseas school trips be cancelled while people over the age of 70 or those with pre-existing serious medical conditions have been told not to go on cruises.
But he stopped short of more extreme measures such as closing schools and banning mass gatherings which have been adopted in Ireland, Norway, France and Italy in an effort to stem the spread of the virus.
Scottish First Minister Nicola Sturgeon said this evening that Scotland was shutting down public events ‘that have the potential to have an impact on our frontline emergency services’.
Mr Johnson said the UK would not close schools yet even though government advisers admitted the move would help stem the outbreak.
Advisers said the length of closure necessary to make the measure work could be more than 16 weeks and would at this stage therefore not be feasible.
Chief scientific adviser Sir Patrick Vallance also said today he believed the true number of infections was likely to be 5,000-10,000 already. He estimated that the UK was four weeks behind the trajectory of the crisis in Italy – which has brought the country to its knees.
The peak of the outbreak in the UK might not come for 10 to 14 weeks, the experts said – suggesting it will run into June.
As a result of their manager’s diagnosis, Arsenal’s upcoming fixtures look unlikely to go ahead.
The club is now attempting to track down anyone who has had close contact with Arteta in recent times.
It is not known if Chelsea’s game against Aston Villa on Saturday will go ahead.
A spokesperson for the club said the teenage midfielder became unwell and had the symptoms of a ‘mild cold’ and hoped their staff will be back to work soon.
The statement said: ‘Chelsea men’s team player Callum Hudson-Odoi had a positive test result for Coronavirus returned this evening [Thursday].
‘Chelsea personnel who had recent close contact with the player in the men’s team building will now self-isolate in line with Government health guidelines. These will include initially the full men’s team squad, coaching staff and a number of backroom staff.
‘It is expected that those who did not have close contact with Callum will return to work in the coming days. In the meantime, the men’s team building, one of several separate buildings at our training ground, will remain closed. The rest of our training facility, Stamford Bridge and our other facilities are operating as normal.
‘Callum displayed symptoms similar to a mild cold on Monday morning and has not been at the training ground since then as a precaution. However, his test came in positive this evening and he will undergo a period of self-isolation. Despite testing positive for the virus, Callum is doing well and looking forward to returning to the training ground as soon as it is possible.’
If Arsenal now cannot fulfil their fixtures in the next two weeks because their players are self-isolation, that also puts their FA Cup quarter-final with Sheffield United on March 22 at risk.
Arsenal said in a statement: ‘It is clear we will not be able to play some fixtures on their currently scheduled dates. We will update supporters who have tickets for forthcoming games with more information as soon as possible.’
Arsenal’s under-23 game on Friday against Tottenham, plus their under-18 against Reading and under-16 against Boreham Wood on Saturday will all be postponed, the club said.
One proposal in tomorrow’s Premier League meeting, which will be held as a conference call tomorrow morning, will be to postpone all games until the international break later this month when they could be rescheduled.
It could also see all the remaining Premier League fixtures played behind closed doors.
Arsenal played Olympiacos in the Europa League a couple of weeks ago, and since then the Greek club’s owner Evangelos Marinakis has tested positive for the virus.