McLaren has also had to change its livery for the 2019 season opener.
Already, Ferrari has unveiled a special 90th anniversary livery to replace the Mission Winnow branding, which came under the spotlight of local health authorities over its links to Philip Morris.
But McLaren also has a new tobacco sponsor for 2019 in the form of British American Tobacco.
In Melbourne, it emerged that BAT's "A Better Tomorrow" branding on the McLaren cars and overalls has been replaced by one-off sponsor 7-Eleven.
Spain's Marca and AS sports newspapers say both Mission Winnow and A Better Tomorrow will be back on the Ferrari and McLaren cars respectively in Bahrain.
A BAT source said the company would study "the laws and regulations in the countries that host the grands prix".