A 32-year-old man was arrested after he spent the night in Worting Road Cemetery and was found with the ceramic image in his possession.
Police have not been able to locate the grave it belongs to and said the theft would "undoubtedly" have "caused tremendous distress" to the family.
Releasing the photo of the baby would not be "in good taste", police said.
"If you know of someone who has had a ceramic photo of a baby stolen from a grave at Worting Road Cemetery in the past couple of weeks, please do ask them to contact us so we can ensure this precious item is returned to them," said PC Neil Plascott from Hampshire Constabulary.
The man, who is not the father of the baby, was arrested on Thursday.
The family of a baby whose photograph was stolen from a grave in Basingstoke is being sought by police.