Peter Mesheau (born in Sackville, New Brunswick) is a politician in New Brunswick, Canada. He represented the electoral district of Tantramar in the Legislative Assembly of New Brunswick from 1997 to 2006.
Mesheau was elected in a tight three-way race to represent Tantramar in a by-election in 1997 to replace Marilyn Trenholme Counsell who had resigned to become Lieutenant-Governor of New Brunswick. Mesheau, a Progressive Conservative received 34.1% of the vote to 33.2% for Liberal candidate Ross Monk to 30.2% for New Democrat Heather Patterson. The leader of the Confederation of Regions Party, Greg Hargrove, was running as a parachute candidate and finished a distant fourth and last place with 2.5%. The margin of victory between Mesheau and Monk was only 39 votes.
Mesheau's victory happened in the midst of a leadership campaign for his party which was won shortly thereafter by Bernard Lord whom Mesheau supported. As a result, Mesheau was appointed to the high-profile role of Health Critic in the shadow cabinet.
The Progressive Conservatives won the 1999 provincial election and Mesheau was named to the cabinet as Minister of Economic Development, Tourism and Culture. Lord restructured the government in 2000 and Mesheau took over the new Department of Investments and Exports. In October 2001 Mesheau was promoted to the high-profile position of finance minister. Following the 2003 election, Mesheau was shuffled to Business New Brunswick, another department which had been carved out of his old Economic Development portfolio and one which had since annexed his old Investment and Exports department.