Assoumani won a fourth five-year term after the country's electoral body on Tuesday declared him the winner of Sunday's election against five opponents.
The army fired tear gas to disperse protesters in the streets of the capital Moroni on Wednesday, while protesters were still on the streets in the north of the capital in the early hours of Thursday.
The interior ministry announced the curfew on Wednesday.
A Comorian government spokesperson blamed supporters of losing candidates for the protests.
"These are things that happen here and elsewhere, especially when we are beaten and we contest the results," Comorian government spokesperson Houmed Msaidie told Reuters.
Msaidie said several demonstrators were arrested.
Assoumani's opponents have said the election was tainted by voter fraud, saying there were instances of ballot stuffing and of voting ending before the official closing time. The government has denied those accusations.
Assoumani has ruled Comoros since first coming to power through a coup in 1999. He garnered 62.97% of the vote in the latest election, according to the national electoral commission.
With a population of about 800,000 people, Comoros has experienced around 20 coups or attempted coups since winning independence from France in 1975 and is a major source of irregular migration to the nearby French island of Mayotte.
The United Nations High Commissioner for Human Rights urged for calm and appealed authorities to practice restraint in the wake of protests.