Air Canada operates about 16 weekly flights to four Cuban destinations from Toronto and Montreal that will be on hold during the fuel shortage, the airline said.
The airline said it would monitor the situation to determine when to restart Cuba service.
WestJet and Air Transat – two other Canadian airlines – have not yet suspended flights.
The move comes amid increasingly dire circumstances on the island and continued threats from US President Donald Trump.
The country has faced rolling blackouts, leaving Cubans struggling to cope without reliable electricity.
The confiscation of sanctioned Venezuelan oil tankers by the Trump administration has started to worsen the fuel and electricity crisis in Cuba.
Trump has also threatened tariffs on countries that supply oil to Cuba, saying in part that Cuba “will be falling pretty soon” as Venezuela no longer sends oil or money to its long-time ally.
The tariffs could target any country “that directly or indirectly sells or otherwise provides any oil to Cuba”.
Cuba Foreign Minister Bruno RodrÃguez Parrilla recently said that the Caribbean nation had “the absolute right to import fuel” from any willing exporter “without interference or subordination to the unilateral coercive measures of the United States”.