The Friary School has put up the sign after motorists looking for a nearby testing centre kept driving onto the grounds and asking children if they were in the right place.
The testing centre is at University West car park on a road called The Friary, but pupils and parents have revealed that some drivers have rolled down their windows to ask about the test centre.
The school said in a tweet: "Covid testing in Lichfield. It is at the Friary car park in town - not the school.
"Definitely not a good idea to come into a school if you think you have Covid."
A parent, who didn't want to be named, said: "It’s not good if people who think they have Covid-19 are driving onto a school, leaning out of car windows and asking children if they’ve gone to the right place.
"Clearly this is putting our children at risk. People should really check first before they set out.
"And if they think they’ve got coronavirus, they definitely shouldn’t be talking to children."