The sign appeared in Castlederg, urging people to stay away from shops from next Friday.
A DUP councillor said he has reported the sign to the PSNI.
It comes after controversy over flags which remain in the town after a band parade in September.
The flags have been causing tension, with the matter being raised at a recent council meeting.
The sign, erected by an unnamed group, has been spotted on the wall of Priest’s Lane car park in the town.
It states: “Firstly, we have nothing against Protestant culture, but the way our town looks is unacceptable.
“We understand that it is a minority that is behind the erecting of flags, respect goes both ways.
“So from Friday the 29th of November, we call for a full boycott of all businesses in Castlederg and surrounding areas and also a boycott of all religious ceremonies over Christmas in the town centre.”
The sign that appeared in Castledeg. Photo: Keith Kerrigan/Facebook
Maoliosa McHugh, a Sinn Fein MLA in West Tyrone, condemned the sign.
“The sign erected and addressed to the people of Castlederg and Aghyaran is absolutely disgraceful, and I want to fully condemn whoever is behind it,” he said.
“Those who erected this offensive sign, whatever their motivation, should immediately remove it and end their anti-community behaviour.
“I also reiterate the call for the removal of flags from the town centre which is a shared space.”
DUP councillor Keith Kerrigan said he had reported the matter to the PSNI.
“I call on those who have erected this sign to remove it immediately,” he said.
“I have requested that the council remove this sign as it is placed on a council controlled car park.”
He added: “Boycotting does not work and I totally condemn this sign being placed in Castlederg and those who felt it appropriate to erect it.
“We need to support all our local businesses and business ratepayers no matter what religious background the owners hold.
“Business owners are not responsible for what is placed on a lamppost outside their premises and to call for a boycott on the mouth of Christmas is reckless and endangers people’s livelihoods.”
At a recent meeting of Derry and Strabane council, a Sinn Fein councillor claimed the band parade in September led to a “proliferation” of flags.
Ruairi McHugh said the flags were disrespectful to the nationalist community and local business owners.
“It’s also disrespectful to those people within the unionist community themselves who don’t want to see their flag flying from lamp posts,” Mr McHugh argued. “So these flags need to come down”.
He added: “I’m not raising this in an effort to curtail anybody’s rights or traditions, if people want to have a parade that’s well and good, but it’s only reasonable to ask that [flags] then be taken down in an acceptable time frame.”