A teenager whose hair was cut off by another bus passenger in Sydney has made a statement to police, who have launched an investigation into the bizarre incident.

The victim was left shaken and in tears following the incident on the route 339 bus, which was travelling from Clovelly towards the city on Wednesday morning.

Police are expected to examine CCTV footage from the bus in a bid to identify a man and a woman who were sitting behind the 19-year-old when a chunk of her long, dark hair was cut off near Moore Park.

Witnesses who spoke to Fairfax Media described the pair as "pasty" and apparently drug-affected.

"The [woman] looked like she was drugged out of her head, class-A whacked. She was completely off her tree," one witness, who did not want to be identified, said.

"The [victim] turned around and asked the man, 'Did you cut my hair?' "

"She was really distressed. There was a good three or four inches cut off and she was obviously sure the guy had done it."

Another passenger said he had deliberately avoided the pair when he got on at Clovelly because they were behaving so oddly.

"She was sitting on his lap sucking her thumb. I thought 'That's a bit weird.' I moved so I wasn't near them," he said, adding that the whole incident was "so creepy".

The woman had dark hair and appeared to be aged in her 20s, while the man appeared to be a bit older, he said. They were both wearing dark clothing.

The pair got off the bus near Moore Park before the driver learnt what had happened. The driver then chased the pair, but they got into a taxi that was last seen heading along Cleveland Street, witnesses said.

A NSW Police spokeswoman said officers had taken a statement from the woman.

State Transit said in a statement that it was aware of the incident and would co-operate with the police.

"The safety of our customers and staff is our number one priority and we do not condone any instances of anti-social behaviour on our buses," it said.

Fairfax Media has contacted the Rail, Tram and Bus Union for comment.

Anyone with information about the identity of the pair should call Crime Stoppers on 1800 333 000.

With Kate Aubusson