The US company reiterated in its Facebook that it has maintained neutrality in the face of the political crisis in the country.
The statement came after some anti-coup activists used its logo and symbol in their social network sites.
"We believe that such acts can be carried out with the intention of pursuing certain political interests", the chain said.
"We emphasise that we have no connection with such actions and we wish to clarify that McThai maintains and will continue maintaining a neutral position in the current political situation in Thailand," it added.
The global food service retailer asked demonstrators to stop using its logo, symbols or trademark and threatened to take "appropriate measures" to protect its rights.
"We wish to request any person who has, in the past, or intends, in the future to use the McDonald's logo, symbol or trademark, to cease and refrain from doing so with immediate effect," read the statement.
On Sunday, several anti-junta demonstrators hid in a McDonald's restaurant in Bangkok after which at least two of them were arrested by the soldiers.