The explosions are thought to represent the deadliest attack in Lebanon since the end of the civil war in 1990.
As Friday prayers ended, a blast hit the al-Taqwa mosque, which is usually attended by prominent Sunni cleric Sheikh Salem Rafii. He was unharmed.
A second blast five minutes later hit the al-Salam mosque in the Mina area.
War in neighbouring Syria has raised sectarian tensions between the city’s Sunni Muslim and Alawite communities.
UN Secretary-General Ban Ki-moon has condemned the attacks and called for calm and restraint.
Sheikh Salem Rafii is one of the most prominent Sunni leaders in Lebanon, BBC Arabic reports from Beirut, and is believed to have been a possible target.
He is opposed to Lebanon’s militant Shia Hezbollah group and has previously urged young Lebanese men to join opposition fighters in Syria.
It is not clear whether he was at the al-Taqwa mosque at the time of the attack, although some reports say he was giving a sermon.
The BBC’s Yolande Knell in Beirut said the cleric was expected to issue a statement after meeting the Muslim Clerics’ Council, the umbrella body for Lebanese Sunni leaders.
Ambulances rushed to the aftermath of the blasts and heavy black smoke covered the sky.
“It was as if there was an earthquake, the whole city seemed to be shaking,” a local resident told Lebanon’s Daily Star newspaper.
Television pictures showed damaged cars on fire, with their windows smashed, and people running through the streets trying to carry wounded people to safety.
Bodies could be seen on the ground and windows were broken on surrounding apartment blocks.
The preacher at the al-Salam mosque – the site of the second explosion – is also an opponent of the Syrian government and its Lebanese ally, Hezbollah, Associated Press reports.
No group has taken responsibility for the latest attacks.
In a statement reported by Lebanon’s National News Agency, Hezbollah strongly condemned the blasts.
The group said the attacks aimed to “sow seeds of strife among the Lebanese and drag them into bickering under a sectarian guise”.
Outgoing Lebanese Prime Minister Najib Mikati and President Michel Suleiman have also condemned the attacks, calling on citizens to unite against violence.
A spokesman for UN Secretary-General Ban Ki-moon said: “The secretary-general calls on all Lebanese to exercise restraint, to remain united, and to support their state institutions… in maintaining calm and order in Tripoli and throughout the country, and in preventing the recurrence of such destructive actions.”
Tripoli, a city of nearly 200,000 people and Lebanon’s second largest, is one of the country’s most volatile sectarian fault lines, with a small Alawite population living in the midst of a Sunni majority.
The Alawite community tend to support Syrian President Bashar al-Assad, with Sunnis mostly backing the rebels fighting him.
The bombs come a week after a massive car bomb rocked a Shia district of Beirut, leaving 27 people dead. The area hit contained Hezbollah strongholds.