"Police will focus on shopping centers, too," Police Commissioner General Renatas Pozela told reporters on Thursday.
"It's primarily the function and responsibility of shopping centers' administration to ensure compliance with the lockdown requirements in and outside their shops. So, we'll simply assess and monitor the situation," he added.
Police will analyze material recorded by surveillance cameras to see if people wear masks in shops and observe the ban on crowding, according to Pozela.
Vilnius county police chief Saulius Gagas said there has been "a run on shopping centers" since the morning.
"Therefore, instructions have been given to watch if shopping centers comply with the lockdown requirements," he said.
Under the Code of Administrative Offences, fines for flouting the rules range from 500 to 1,500 euros for private individuals and from 1,500 to 6,000 euros for business managers.
Only shops selling groceries, medicines and veterinary products are allowed to operate under the nationwide lockdown.