The garden centre is registered as a Pokéstop in the location-based reality mobile game meaning when players check in, it provides them with items such as Poké Balls, eggs and potions to heal their Pokémon.
Tapp's said: "We know in the new Pokémon game that we are a poke stop and that's fine and seeing kids out walking is great.
"But please be careful or tell your kids to be careful when walking through our car park with your head stuck in your phone as people bolt through and use us as a roundabout and sometimes very fast. Last thing anyone wants is anyone getting hit by a car. It's a real worry.
"Also please respect our opening hours. When we are closed, our alarm systems and CCTV are on. Coming past our gates or into our car park (sometimes one of our gates is open as we live here to) will set our systems off and I'm sure you do not want the drama, police and everything that comes with trespassing. Please pass the message on. Thankyou."
Meanwhile, Cardwell Garden Centre, near Gourock has joined the fun by offering prizes to people who post photos of captured Pokemon critters on their Facebook page.