No, it does not come with a picatinny mount as its meant to be mounted to the T.M.P.R. prism sight.
Shotgun recoil is not a problem, but this particular FastFire model is intended for use with the Burris T.M.P.R 5x optic.
For shotguns, Burris makes the SpeedBead mount for the FastFire II and FastFire III - the mount fits between the stock and receiver, and is made for a variety of shotguns,
https://www.opticsplanet.com/burris-speedbead-mounts.html
FastFire II:
Code: BR-RD-FastFire-300233
MPN: 300233
UPC: 000381302335
https://www.opticsplanet.com/burris-fastfire-w-picatinny-mount-4-moa-dot-mat-fastfire-sight.html
FastFire III:
Code: BR-RD-FFIII-300235
MPN: 300235
UPC: 000381302359
https://www.opticsplanet.com/burris-fastfire-iii-red-dot-reflex-sight-w-optional-picatinny-mount.html
If the SpeedBead base is not available for your shotgun, you may be able to get a mount for it and use the FastFire with the picatinny/weaver mount. Give us a call and we'd be glad to help you out - 1-800-504-5897.
Mark H.