Local officials estimated the turnout to be about 60%, with only a few minor incidents of violence.
It is the first stage of elections to four Indian states in what is being seen as a critical test for the ruling BJP led by Prime Minister Atal Behari Vajpayee.
In Punjab, the BJP and its local ally, the Shiromani Akali Dal - which rules the state - are facing a challenge from the opposition Congress party.
Correspondents say the main issue in this year's electoral campaign has centred on corruption in public offices, and exit polls indicated that the opposition may be heading for victory.
Security
Heavy security was in place across the state in which 918 candidates are contesting 116 seats.
There were also reports of complaints by Hindu voters in some areas who alleged that their names had been deliberately deleted from voters' lists.
On the frontline
Punjab was badly hit by Sikh separatist violence for more than a decade in the 1980s.
It is also a frontline state on the border with Pakistan, which has been locked in a tense confrontation with India since December, when the Indian parliament was attacked.
India blamed Pakistan-based militants for carrying out that attack - a charge that was dismissed by Islamabad.
Several villagers living close to the border moved away amid fears of a war, but it is not clear how the issue will play in the polls.
Electronic voting machines are being used for the first time in the more than 19,000 polling stations throughout the state.
Poll test
Voting is due to take place in the states of Uttar Pradesh, Uttaranchal and Manipur in the north-east over the next week - the polls have been staggered to allow security forces to be moved across the country.
Analysts say the polls will test the popularity of Mr Vajpayee's government, which is made up of an alliance of more than 15 parties.
Final results are not expected to be known before 24 February.