Remove wood, debris and junk piles that are stored near the greenhouse. If you must keep these in place, elevate the piles 12 inches off the ground. Clean up the garden growing next to the greenhouse, removing all plant debris that can act as safe hiding places for mice. Prune shrubs growing next to the greenhouse so the branches are at least 12 inches off the ground. Seal trashcans and take in pet food after your pets finish eating. Don't scatter bird seed and breadcrumbs for wildlife.
Clean up plant debris inside the greenhouse. Remove decaying matter, including fruit droppings, from potted plants. Prune any seed pods that can be a food source. Store bone meal, bulbs and seeds in rodent-proof containers.
Examine the greenhouse for openings that allow mice entrance. Seal cracks and holes in the foundation and replace any missing or broken windowpanes or doors. For a quick fix, crumple up aluminum foil and stuff it in the cracks and holes, or cover them with a fine wire mesh.
Open the door and turn on a high-frequency sound device -- which is sold for this purpose -- to scare the mice from the greenhouse. Open windows and vents without screens so they find an easy exit. Keep it on for several hours, and check the next day for signs of mice. Repeat as necessary.
Set up snap-style mousetraps, if you don't mind killing the mice, using a bait such as peanut butter. Set the traps along the floor of the greenhouse where you see mouse droppings and other signs of mice. Set the traps near their favorite potted plants. Check the traps each day. Discard the dead mice and reset until the last nuisance mouse is caught.