Thompson's resignation comes at a time when the company is trying to raise cash to cut its $3 billion debt as it faces curbs on drug pricing from governments and companies.
Reuters reported earlier this month that the company was discussing alternatives to a leveraged buyout, including selling a minority stake to a private equity firm.
The talks came after negotiations about selling the company failed to produce a deal that would be acceptable to its board, sources told Reuters.
A search process for a new CEO is underway, the company said.
Concordia, which had a market capitalization of C$270.1 million ($202.46 million) as of Thursday close, sells drugs for conditions ranging from malaria to heart disease.
Concordia's Toronto-listed shares were up 18 percent at C$6.16. The company's U.S.-listed shares were up 19 percent at $4.73.
Reporting by Anet Josline Pinto and Akankshita Mukhopadhyay in Bengaluru; Editing by Anil D'Silva and Don Sebastian