The 2,000-year-old sling stones, which were taken from the ancient city of Gamla on the Golan Heights, were left last week in a bag in the courtyard of the Museum of Islamic and Near Eastern Cultures in Israel's southern city of Beersheba, said the IAA.
"These are two Roman ballista balls from Gamla, from a residential quarter at the foot of the summit," the thief wrote in a note distributed by the Authority.
The thief did not detail the nature of his or her misfortune.
The Antiquities Authority said nearly 2,000 such stones were found in Gamla. They were used by the Romans against the Jews attempting to prevent the conquest of the hilltop city.
This was not the first plundered antiquity to be returned, said the Authority, noting that a Tel Aviv resident had held an ancient coffin in his bedroom before realising its "morbid nature".