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.
The European Commission said it had deployed rescue teams from Italy, Greece and Romania to help with the search efforts, while teams were also sent from Kosovo and Montenegro.
Tuesday's earthquake has been described by the authorities as the strongest to hit Albania in decades.
It struck at 03:54 (02:54 GMT) and was followed by powerful aftershocks.
In Thumane, a five-storey apartment building collapsed.
Dulejman Kolaveri, a man in his 50s, said he feared his 70-year-old mother and six-year-old niece were trapped inside because they had lived on the top floor.
"I don't know if they are dead or alive," he told AFP news agency, his hands shaking. "I'm afraid of their fate. Only God knows."
In Durres, a woman called Bukuri Morina and her family of 10 joined thousands of others to spend the night in tents at the soccer stadium.