Pinera stated that he planned to present a proposal -- which would need Congress approval -- for "the health of all the inhabitants of Chile" to postpone the April election until mid-May.
Chile has registered record numbers of coronavirus infections in recent weeks.
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With new, more contagious, virus variants spreading across Latin America, cases have soared in Chile despite the South American nation's impressive vaccination drive.
Chile has also begun a strict lockdown for more than 80 percent of its population, with shopping trips for even basic products banned during weekends.
The election -- now scheduled for May 15 and 16 -- will choose the 155 members of the Constituent Assembly which will rewrite the constitution dating from the rule of military dictator Augusto Pinochet.
One of the key demands from protesters who rose in October 2019, leading to months of protests against social inequality, was to rewrite the constitution. Chileans voted overwhelmingly in favor of this measure in an October referendum.
Chileans return to the polls on November 21 to elect a successor for Pinera, who is unable to stand for re-election.