The cruel act was carried out at about 2.15pm on Friday in front of shoppers in Stirling, Police Scotland said.
The man, who was walking with a woman, is described as being aged in his late 20s and he was wearing a blue jacket and jeans.
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.
"This kind of incident is not only unacceptable but completely illegal. We would remind people that pigeons are fully protected by law and offences against wild birds are taken seriously by the police and courts.
"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."