A Muslim woman had her headscarf stolen and a beer bottle thrown at her during an alleged assault at a Perth shopping centre, a group that monitors Islamophobia in Australia has said.

Police confirmed they were investigating the assault on the woman, 34, at the Beeliar Village Shopping Centre on Friday December 16.

The Islamophobia Register Australia, a group which encourages people to report anti-Muslim sentiment, said the incident began with a verbal exchange between the pair.

"The incident quickly escalated with the man allegedly calling the woman a 'f***ing Muslim' and after she started walking towards him, he allegedly smashed his beer bottle, hitting her back and shoulders," Islamophobia Register Australia president Mariam Veiszadeh said.

"A physical fight then allegedly broke out between the pair.

"The woman's headscarf allegedly came off during the physical altercation and the offender then allegedly ran off with it, dumping it later near the shopping complex."

Witnesses came to the woman's aid after she was assaulted, Ms Veiszadeh said.

Police were unable to confirm the racial slurs or whether the attack was Islamophobic, but said they were investigating an assault outside a supermarket in which a man threw a beer bottle at a woman.

The woman was not injured, police said.

The man is described as between 25-35 years old, between 175 and 180 centimetres tall, with a slim build and short blonde hair.

Anyone with information has been urged to contact police.