Runaway championship leader Max Verstappen, chasing an unprecedented 11th win in a row, was third in session one but only eighth in the second.
"Ferrari is very fast, I think we're just way worse than we expected," said the Dutch 25-year-old.
Team-mate Sergio Perez, last year's winner on the Marina Bay layout, was seventh in both and struggling with the rear end of the car.
"Every braking zone I feel like I'm going to crash. The rear is just stepping out massively," said Perez over the team radio.
"We did expect the Ferrari to be very strong around here," he told Formula One television. "We're just too far away. Hopefully tomorrow we are able to close the gap a bit more but we do expect quite a challenge."
Red Bull have won the last 15 races, and are expected to be fighting for pole again on Saturday, but they had already identified Ferrari as their major rivals coming into the weekend.
The Italian team lived up to expectations, Leclerc leading a one-two in the late afternoon and the positions then reversed later on.
George Russell was third for Mercedes in session two, with Aston Martin's Fernando Alonso fourth.
Seven times world champion Lewis Hamilton was fifth fastest for Mercedes with McLaren's Lando Norris sixth.
'VERY TIGHT'
"I think this track is going to be one of the toughest of the season for us," Red Bull team boss Christian Horner told Sky Sports.
"The characteristics don't play naturally to the strengths of the car and we're going to have to be right at the top of our game to keep this winning momentum going.
"You can see Ferrari look quick, McLaren look like they're there, Mercedes are there as well so it could be very, very tight this weekend."
Leclerc started on pole position in last year's night race on the Marina Bay street circuit and led Friday's session one with a best time of 01:33.350 seconds.
Team-mate Carlos Sainz was 0.078 slower, with yellow flags warning drivers of monitor lizards on the track.
The reptiles stayed away in the second session, with Sainz lapping in a best time of 01:32.120 seconds and 0.018 faster than Leclerc.
"The car looks a bit more competitive than we had expected on a track like this, but we shouldn’t get carried away because I think that our competitors are not showing their true pace yet," said Leclerc.
Verstappen was 0.732 slower than the Spaniard on a shortened track with two fewer corners than before due to construction works.
The Dutch driver, who has yet to win in Singapore or start on pole in the city-state, leads Perez by 145 points after 14 of 22 races. Red Bull could take the constructors' championship on Sunday if results go their way.
McLaren have brought a big upgrade to the race and Norris said it was working well.
"It’s a nice improvement from what we had. I think it’s done everything that it should have done," he said. "I think the pace is reasonable. We might not be as good as Ferrari, but we’re in a good fight for a good position otherwise."
Alex Albon was last in the second session for Williams after being sidelined early on by a power unit problem.
"Aside from the issue, the car hasn’t felt too bad and I don’t believe we’ll suffer from any penalties," said the Thai racer.