Wakefield Council said it had issued fixed penalty notices of £1,000 each to two businesses in January.
The council did not name the venues concerned, but confirmed that they were in Wakefield and Castleford.
Under lockdown restrictions, barbers and hairdressers are not classed as essential services and are not scheduled to reopen until April 12.
That date, which was set by the government, remains subject to change and is likely to depend on coronavirus infection rates remaining low.
In a report going before a full council meeting this week, the authority's Cabinet member for communities, Maureen Cummings said: "Licensing Enforcement (teams) have continued to support the council with regards to complaints made in relation to Covid-19 breaches.
"Licensing Enforcement, along with anti-social behaviour (ASB) case officers, visited and dealt with a large number of relevant complaints, and in January alone issued the following enforcement notices and penalties:
"Two separate barber shops in Wakefield and Castleford were found to have continued to operate during lockdown measures, where licensing enforcement and ASB Case Officers issued two Fixed Penalties (£1000 each) and two prohibition notices."
Coun Cummings said that upon entering the Wakefield barbers, an "ad hoc barber's chair and equipment was found in a rear room, with notable amounts of hair cuttings on the floor."
Local Democracy Reporting Service