I once shipped a larger painting and frame as air cargo on United LAX-SFO. It was to go on a specific flight, the flight I was taking. I retrieved the cargo at the back side of the airport, not the passenger terminal.

Several possibilities.

1. See if the artwork is a painting and can be rolled up after removal from the frame.
2. Properly pack it in a box and ship it as luggage or air cargo.
3. Properly pack it and ship it UPS or Fedex.
4. See if there is a canvas shopping bag that the artwork can fit. See if you can bring it on board based on the thickness is not very thick so it's a 28" x 36" x 2.5"