The cautious estimation of reopening prior to the Spring Bank Holiday on 31 May had previously been made by Mark Drakeford.
Drakeford, however, told BBC Radio Wales that he felt up to 30 people would be able to meet indoors from 17 May if progress tackling the virus continued.
The country has the lowest coronavirus case rate in the UK and the highest percentage of its population vaccinated, compared to the other UK nations.
Reopening date
Drakeford said: "It is my assessment that the hospitality sector - bars, pubs, restaurants and cafes - will be able to open indoors from 17 May.
"Together with all other tourist accommodation, indoor entertainment and attractions."
This would mean pubs and bars in Wales could reopen indoors on the same day English venues hope to be able to reopen for inside trade.
However, he noted the relaxing of rules from 17 May would be for the next Welsh Government to confirm at the next lockdown review on 13 May.
Parties are currently campaigning ahead of the 6 May Senedd election.
Critics have accused the First Minister of bringing forward a relaxation of rules - including soft play for children to 3 May - for the purposes of an election boost.
Drakeford told the BBC: “The virus doesn't know there is an election on, and I don't think it would have been right not to have given those indications.”
Pubs, bars and restaurants will reopen for outdoor trade from Monday 26 April, alongside outdoor hospitality and limited indoor service in Scotland.
Commercial hope
UKHospitality director for Wales Dave Chapman welcomed the news for businesses and said it "offers clarity and commercial hope, and reflects positively the medical evidence".
Businesses had previously described their frustration about a lack of clarity over reopening dates to The Morning Advertiser.
The 17 May reopening date is also key for hospitality businesses in Scotland as that is when they will be permitted to serve alcohol indoors.
