A Melbourne couple sleeping in bed were woken by teenage bandits armed with golf clubs and pretending to be police.

During the home invasion, which took place about 3.40am on Sunday in Glen Iris, teenagers allegedly told the couple to get on the floor before stealing phones and an iPad and drove away in the couple's silver Mercedes.

A 13-year-old Packenham girl was charged with aggravated burglary and will appear in a children's court, but the rest of the intruders remain at large.

The female victim told Seven News anonymously the experience was "terrifying".

"In fact you almost can't believe it's real. It feels quite surreal, as if you're in a horrible nightmare," she said.

"They came around the door, shone torches and they shouted 'police, police, get on the floor'."

No one was injured during the burglary, and the vehicle is yet to be found.