The two were among dozens of people filmed jumping over a wall of the facility in the capital, Nairobi, drawing public condemnation.
While under arrest they said they had planned the escape because they were not getting tested for the virus.
All bars in Kenya have been ordered to close, to halt the spread of Covid-19.
The pair, who are now awaiting charges, had complained that they couldn’t afford to pay for their confinement out of their own pockets.
More than 400 people are under forced quarantine in the country, which lasts for an initial period of 14 days – though this has been extended twice at some centres.
Some are being held because they flouted curfew orders while others have been detained on arrival from abroad.
Many fear they are at greater risk from coronavirus inside, saying poor hygiene is widespread and overcrowding makes social distancing impossible.
As many as 50 people out of 200 escaped from Kenya Medical Training College’s quarantine facility according to local reports, but officials have not confirmed the numbers.
Local police boss Muthuri Mwongera said that he was waiting for the director of public prosecution’s office to charge the two suspects who had been arrested at a bar in the Roysambu area, north of the city.
“A majority of those who escaped had been arrested around this area before being taken to quarantine and so we know we will arrest more with time,” Mr Mwongera said.
