Welsh Government says firms who make their own decision to shut could still get access to the Local Lockdown Business Fund.
Further details have been published on the £60m fund for firms in those areas hit with additional restrictions.
There are two types of grants, the Local Lockdown Discretionary Grant and the Local Lockdown Non Domestic Rate Grant - but concerns were raised that some businesses could be frozen out.
This is because businesses that chose to close but are not required to were marked as not eligible for any money.
That could exclude large areas of the tourism sector and some hospitality operators who rely on visitors and have been hit by the restrictions on travelling into and out of counties in lockdown. Many have shut because the business is simply not viable without visitors.
Business Live raised this with the Welsh Government.
They responded, saying: "We are exploring our options for how these schemes can be flexible.
“Applications will be considered on a case by case basis and local authorities will have discretion on allocating funding including for businesses closed on a short-term basis.”
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Mark Drakeford also yesterday said they would look at businesses impacted by a local lockdown but not actually trading within the locked down area.
Under the grants eligible Retail, leisure and hospitality businesses in Wales occupying properties with a rateable value of between £12,001 and £51,000 could access a grant worth £1,500.
A £1,000 grant will be available to eligible businesses that have a rateable value of £12,000 or less.
Janet Finch-Saunders MS – the Member of the Welsh Parliament for Aberconwy – has also raised concerns the scheme will be administered on a first come, first served basis.
She said: “It is evident that Mark Drakeford’s administration has learnt nothing from mistakes made earlier this year, when grants faced an instant deluge of applications leading to needless confusion, errors and upset for many North Wales businesses owners.
"This cannot be allowed to happen again."
She also questioned if the value of the support would do anything to save many enterprises.
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She said: "It is clear that this equates to mere pennies when compared to what is needed to prevent local residents from losing their livelihoods."
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She has also asked for a review into the decision to enact a rateable value cap of £51,000, saying this would exclude some large hotels in resorts like Llandudno.
Welsh Government has also launched an £80m fund which will support firms with projects that can help them transition to the economy of tomorrow.
There will be £20m ring fenced to support tourism and hospitality businesses who are facing particular challenges as they enter the winter months.
- Go here for details