Many Singaporeans took to using #NotMyPresident in their social media posts, a hashtag that first gained popularity among those rallying against Mr Donald Trump after he won the United States' presidential election previous year.
Mdm Halimah's supporters note that she is qualified for the role and point to her track record of over 40 years in public service.
The returning officer declared Halimah Yacob, 63, elected on Wednesday after nominations closed.
But Yacob emerged after the elections department disqualified the other four candidates, of which two of them are not Malays.
If the election had been held, all citizens would have been eligible to vote.
The other two contenders, Salleh Marican and Farid Khan, were both denied eligibility, having fallen short of a constitutional rule that required any candidate from the private sector to have led a company with shareholder equity of at least 500 million Singapore dollars ($372m).
Reacting, Yee Jenn Jong, opposition politician, said it would have restored some of the lost moral authority if she had won her opponents through popular votes.
Displays of dissent are rare in Singapore, one of the richest and most politically stable countries in the world.
The incoming president, who is to be sworn in on Thursday, appeared unfazed by the controversy.
Yusof was president between 1965 and 1970, the first years of Singapore's independence following a short-lived union with neighboring Malaysia, but executive power lay with Lee Kuan Yew, the country's first prime minister.
"Although this is a reserved election, I'm not a reserved president", Halimah said in a speech at the election nominations office.
Yacob addressed the nation shortly after her announcement as president.
"Whether or not there is an election or no election, my promise is to serve everyone and I will serve with great vigour, with a lot of hard work, with the same passion and commitment".