From the DNRE website:
Is it legal to take feral swine?
Yes, if you are legally hunting game during an open season (of any type) and see a feral swine you may pursue that animal if you wish, following all the regulations of the open season which you are hunting. (Please note: There is an open season of some species 365 days of the year.) For open seasons and regulations, please view the most current Michigan Hunting and Trapping Guide.
What is the new law, Public Acts 69-71 of 2010?
The new law does not establish a hunting season on feral swine. Public Acts 69-71 of 2010 declare feral swine a nuisance species and allow for the opportunistic take of any free-ranging pig running at large. Under this law, a person with a concealed pistol permit (CPL) or valid hunting license can kill swine running at large on public property; landowners or other authorized persons can kill swine running at large on private property; and local animal control officers and law enforcement can kill swine running at large on either public or private property.
When can I legally shoot a feral swine?
Any time during regular hunting hours and when actively night-hunting raccoon, opossum, fox and coyote. (Please be sure to follow all day and night hunting regulations for the season in which you are hunting game. Refer to the current Michigan Hunting and Trapping Guide for details.)
What type of hunting license do I need to pursue feral swine?
Any type of valid hunting license or a concealed pistol permit is needed on public property. Possession of either of these allows the holder to be in legal possession of the firearm associated with the license or permit on public land.
If I have a CPL, do I also need a hunting license?
No, you do not need a hunting license in conjunction with the CPL.
Can I shoot feral swine on private property?
If you are the landowner or have permission of the landowner, you may shoot feral swine on private property at any time. It is not necessary to possess a hunting license or CPL to kill feral swine on private land.