The government has now said it will cater for the costs of quarantining patients in state facilities.
"The cost of targeted testing and quarantine in government facilities shall be met by the government," Kagwe said on Wednesday.
This is a relief to Kenyans who had complained about being asked to pay quarantine costs.
Kenya has recorded 47 new coronavirus cases, bringing the number to 582 people.
A total of 32 are from Mombasa while 11 are from Nairobi, two in Busia and one each in Kiambu and Kwale.
In Nairobi, five cases were from Eastleigh.
Kagwe said the cases in Mombasa are mainly in Old Town, with 18 cases.
Kagwe said 31 are male and 16 female.
Another eight people have been discharged, bringing the total discharged to 190.
On a sad note, another two people have died. They are from Mombasa.
This brings the number to 26, the number of deaths.
Meanwhile, the government has locked down Eastleigh and Old Town as coronavirus cases surge.
There will be no movement within the areas effective Wednesday at 7pm for 15 days, Kagwe said.
"You cannot leave the area to go to another area. This will take place for 15 days," he said.
Kagwe said public transportation will also not be allowed to go to those areas.
"This is to protect those within those areas," Kagwe said.
