A man approached Finsbury Park mosque in north London at about 4.15 am on May 26 several times, before throwing the bag over a gate and onto the steps. The man then ran off towards Rock Street.
He is described as being in his late 30s, white, bearded and around 5ft 9ins tall.
Officers said he was wearing a light-coloured woollen hat, light-coloured coat with a folded-down collar, light-coloured trousers and dark shoes.
Detective Inspector Ralph Coates of Islington Community Safety Unit said: "We take hate crime extremely seriously as we know how destructive these offences can be, both to individuals and to communities.
"I would urge anyone who recognises this man or has any information that will help the investigation to contact police."
Anyone with information about the incident or who can identify the man should contact Islington Community Safety Unit on 020 7421 0281 or call 101 quoting CRIS 2712630/16.
Additional reporting by Press Association