The announcement was made following the biggest antigovernmental protests on the Communist-run island in decades.
Thousands took to the streets on Sunday to protest over food and medicine shortages, price increases and the government’s handling of Covid-19.
There will be no limit on such goods brought in by travellers from Monday. However, the measure is only temporary and has been derided as “too little, too late” by critics of the government.
Prime Minister Manuel Marrero Cruz announced the change on Wednesday at a meeting broadcast on state television.
“No, we don’t want crumbs. We want freedom,” government critic and journalist Yoani Sánchez tweeted shortly after the announcement.
“Blood wasn’t spilled on Cuban streets in order to import a few extra suitcases.”
The protests, which started on Sunday, were not only the biggest but also the most widespread to be held in Cuba in decades.
Dozens have been arrested nationwide since the unrest began. Authorities confirmed on Tuesday that one man had died.
News of the protests spread on social media, where demonstrators posted live footage of gatherings across the country.
Mobile internet access was introduced in Cuba in the last few years but is provided by a state-run company.
In the wake of the protests, there was an internet blackout which many blamed on the government trying to block communications.
AFP news agency journalists reported that Cuban authorities had restored access to the internet on Wednesday. However, some messaging and social media platforms reportedly remained blocked on 3G and 4G, including Facebook, WhatsApp and Twitter.
Streets in Havana were calmer on Wednesday, although there was a heavy security presence.
Arrests seem to have continued in the country in recent days. Cuban YouTuber Dina Stars was conducting an interview for a Spanish broadcaster on Tuesday when she told the channel that security forces had come to take her away. She later posted about it on Instagram.
And Reuters obtained footage from Tuesday which it said was of a young man in the south-eastern town of Gibara being arrested.
The protests come amid a severe economic crisis. Tourism, one of the most important sectors, has been devastated by the restrictions on travel during the Covid pandemic.
Sugar, which is mostly exported, is another key earner for Cuba. But this year’s harvest has been much worse than expected.
As a result, the government’s reserves of foreign currency are depleted, meaning it cannot buy in imported goods to supplement shortages, as it would normally do.
Cuba has blamed the US and its economic sanctions for the protests and Cuba’s wider problems. On Wednesday, the US called for the release of all peaceful protesters detained in Cuba during recent unrest.