The turnout was reported to be brisk around capital Colombo and in the Sinhala-dominated areas, but light to moderate in the Tamil regions of the northern part of the island where polling was marred by pre-dawn bomb blasts and allegations of vote rigging.
The counting will start on Tuesday night with early trends expected to be available around midnight.
Rajapaksa, 64, had called the election two years ahead of schedule, apparently to cash in on the military victory over the LTTE, but an acrimonious campaign was witnessed between him and his former military chief Fonseka.
Fonseka, the joint opposition candidate, said he was unable to vote as his name was not on the electoral list, prompting statements from the ruling party lawmakers that he could face disqualification.
However, Elections Commissioner Dayananada Dissanayaka released a statement a short while ago stating that a candidate need neither be a registered voter nor cast his vote in order to be eligible to run for office. Dissanayaka said Fonseka, 59, would not face disqualification if he was duly elected.
The final results are expected on Wednesday morning.