The 6.4 magnitude tremor struck 34km (21 miles) north-west of the capital, Tirana, as people slept in their beds during the early hours.
Most of the deaths occurred in the coastal city of Durres and the town of Thumane, close to the epicentre.
Tents have been set up for those left homeless by the disaster.
Prime Minister Edi Rama promised that rescuers would "continue to search patiently and thoroughly to the end".
The government has declared Wednesday a day of mourning.
