“We were devastated. It just brought us all to the floor,” said Ms. Licon, who was alerted to the theft by a custodian who noticed the vacant spot on the shelf. “We’re a small museum, and we just don’t acquire pieces like this.”

The police report estimated its worth at $5,000, but described the artwork as “invaluable.”

“There’s almost no way to put a value on something like that because there’s no market,” said Jack Klasey, a longtime museum volunteer and local historian.

The theft occurred at the beginning of the museum’s busiest month. In December, groups of schoolchildren and others streamed through the museum — past the Barnard sculptures, tributes to local sports heroes and artifacts honoring three Kankakee County natives who served as Illinois governor — to admire Christmas trees decorated by civic groups.

“I saw it in the newspaper and just thought, ‘Who would go into that small museum and walk out with that hand?’ ” said Trisha Campbell, who stopped by with her co-workers days after the theft was discovered to browse the Gallery of Trees at the museum.

In addition to being outraged, museum visitors were perplexed. “I think it’s kind of crazy,” said Kelly Lambert, a college student whose aunt works at the museum. “Why would someone want to walk off with a fake Abraham Lincoln hand?”

Since the theft, Ms. Licon said curators had removed other small Barnard pieces from the display, fearing that they might also disappear. “Now we’re paranoid,” she said. “And we’re wondering: Is this person going to come back?”

There is a precedent for stealing Lincoln memorabilia, said James Cornelius, a curator at the Abraham Lincoln Presidential Library and Museum in Springfield, Ill. In recent decades, Dr. Cornelius said, manuscripts and books with ties to Lincoln have been reported stolen. And more dramatically, in the 1870s, a band of criminals failed in an attempt to steal Lincoln’s body from his tomb in Springfield.