The advice was issued after a number of schools banned photography on their premises to protect pupils who were adopted or in foster care.
Earlier this week a father complained he was threatened with arrest at a school in Leicestershire.
Information Commissioner Christopher Graham said such photos did not breach the Data Protection Act.
BBC technology correspondent Rory Cellan-Jones says it is a common experience at this time of year for proud parents trying to take pictures of their children performing in nativity plays to be be told by teachers that photography is banned.
The Information Commissioner's Office has released guidance for schools after receiving numerous queries from parents.
The regulator said photos for personal use were not covered by the Data Protection Act.
Fear of breaching the law should not be used to to stop people taking pictures or videos, he added.
Mr Graham said: "Having a child perform at a school play or a festive concert is a very proud moment for parents and is understandably a memory that many want to capture on camera.
"It is disappointing to hear that the myth that such photos are forbidden by the Data Protection Act still prevails in some schools."
He added: "A common sense approach is needed. Clearly, photographs simply taken for a family album are exempt from data protection laws.
"Armed with our guidance, parents should feel free to snap away this Christmas and stand ready to challenge any schools or councils that say 'bah, humbug' to a bit of festive fun."
Parents should be free to photograph their children in nativity plays, the Information Commissioner has said.