Ishwar Singh, another senior police official, told reporters that the explosion was caused by a single bomb.
No one has claimed responsibility for carrying out the attack.
Indian television news footage showed at least one body lying on the floor of the cinema, which was strewn with shards of broken glass and blood stains.
Pardeep Kumar, another witness, told Reuters news agency: "The movie had just started when there was a big noise followed by smoke. It was total chaos after that."
Al Jazeera's Matt McClure in New Delhi said that the blast happened in a predominantly Muslim area of the city but that the cinema audience would have been mixed.
Punjab is India's only Sikh majority state.
The blast came just days after two people were killed and nearly a dozen injured in a bombing near a Sufi Muslim shrine in the northern state of Rajasthan.
Authorities said Thursday's explosion, which took place in the town of Ajmer, was caused by a small bomb packed inside a tin lunch box which detonated during evening prayers.