The act was carried out in front of shoppers in Stirling, Police Scotland said. The man, who was with a woman, is described as being aged in his late 20s and wearing a blue jacket and jeans. The incident happened at around 2.15pm last Friday.
James Leonard of the RSPB said: "This was a horrendous incident that took place in a busy city centre street and must have been deeply upsetting for those who witnessed it.
"I would urge anyone who can assist in identifying this person to come forward and speak to police as soon as possible so they can be brought to justice for this callous act."
Constable Malcolm O'May, wildlife crime officer for Forth Valley, said: "This was a unnecessary act of cruelty which resulted in the death of the pigeon.
"I am appealing to anyone who has information as to the identity of this male to contact us."