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Extra cash support for hospitality businesses still affected by Covid restrictions has also been announced.
Mr Drakeford said the funding would "support firms and safeguard jobs".
The support is available to businesses such as pubs, clubs, restaurants and late-night entertainment venues.They can claim up to £25,000 to help them through to the end of June as they prepare for re-opening and more normal trading conditions.
The news comes after there were calls from some in the hospitality industry for all significant restrictions on trading to be lifted before July.Supply chain firms, events and conference venues not covered by the Welsh government's Cultural Recovery Fund (CRF) can also apply for support.
Mr Drakeford said the cash was part of a £200 million package earmarked for the incoming Welsh government to help businesses affected by the pandemic.
"We know the restrictions have helped to keep us all safe but they have had a big impact on Welsh businesses, which is why we are making more funding available to support firms and safeguard jobs," he said.Welsh Labour, under Mr Drakeford, won last week's Senedd elections.
The Welsh Labour leader had faced criticism during the election campaign for not announcing the extra financial support for the hospitality sector. At the time, he said "election rules" prevented him from releasing the cash.
