Mark Drakeford said it would be for the incoming Welsh Government to confirm the reopening, but the main opposition parties have already committed to the same date if they win the May 6 Senedd election.
Other changes expected by May 17 include reopening indoor entertainment venues and attractions, with more changes “subject to the public health situation remaining favourable”.
The dates for indoor hospitality and tourism accommodation brings Wales in line with the reopening dates in England
Wales has the lowest level of virus infections in the UK and is third in the world in terms of vaccine delivery.
On Thursday, Mr Drakeford said: “At the last three-week review, I set out a forward-look of how the restrictions could continue to be lifted in the weeks ahead, if the public health situation remains stable.
“It will be for the incoming Welsh Government to confirm these arrangements at the next three-week review, which will be held on May 13 – a week after the election.
“It is my assessment that the hospitality sector – bars, pubs, restaurants and cafes – will be able to open indoors from May 17, together with all other tourist accommodation, indoor entertainment and attractions.”
Mr Drakeford’s indication means Welsh Labour joins the Welsh Conservatives and Plaid Cymru in pledging to reopen indoor hospitality on May 17.
Mr Drakeford said other changes to Wales’ restrictions before the election meant the country will complete its move to Alert Level 3 by May 3.
From Monday, outdoor hospitality can reopen and up to six people can meet outdoors with no limit on the number of households they can come from, not including children under 11 years of age or carers from those households.
Outdoor attractions including swimming pools, funfairs and theme parks, as well as outdoor organised activities and wedding receptions, both for up to 30 people, can also take place.
From May 3, gyms and leisure centres can reopen, and people can form extended households with one other household.
Mr Drakeford said indoor supervised activities for children, indoor organised activities for up to 15 adults like exercise classes, and reopening community centres was also being brought forward from May 17 to May 3.
“The sacrifices we have made continue to show results. By us all working together and sticking to the rules, combined with our vaccination programme, mean we continue to make progress,” Mr Drakeford said.
“Rates of the virus continue to fall and the public health situation is improving.
“Due to these efforts we are able confirm more easing of the restrictions from 26 April and for early May we are again able to bring forward some of our plans.
“However, this progress is dependent on all of us continuing to work together to keep Wales safe.”
Mr Drakeford will appear at a press conference on Friday afternoon to confirm the changes amid accusations from the Tories and Plaid that he is using the briefing to unfairly influence the forthcoming election.
Tory MS Janet Finch-Saunders said the briefing would be “naked electioneering” and called for the chief medical officer to front it, while Plaid leader Adam Price has written to the Government’s Permanent Secretary Dame Shan Morgan asking her to “ensure parity and fair play for all”.