An AFP correspondent saw almost all the entire glass facade of the headquarters of BLOM BANK, one of the country's largest, blown out, with debris littering the ground.
Interior Minister Nuhad Mashnuq told AFP a bomb containing about 3-4 kilos (6.6-8.8 pounds) of explosives had been "placed behind the back wall of BLOM BANK".
"It is clear that the bank was the target," he said.
Mashnuq gave no further details, but in comments to LBCI television channel he said the blast was "different" from other explosions that have occurred in Lebanon over the past few years.
Veteran Druze politician Walid Jumblatt linked the bombing to a law voted in December by the US Congress to impose sanctions on banks that deal with the Shiite movement Hezbollah.
In May, Lebanon's central bank instructed the country's banks and financial institutions to comply with the US law.
Hezbollah's parliamentary bloc warned at the time that the move could push Lebanon towards bankruptcy.
"We have entered a cycle of attacks," Jumblatt told LBC television, and called for a "roadmap between Hezbollah and (Lebanese) banks" to ease tensions.
Signup to our newsletter and follow us on Facebook and Twitter!
Jumblatt also told the Arabic-language newspaper An-Nahar that he had "issued a call for a calm dialogue concerning the American sanctions... but some are refusing that."
The blast "is a blow aimed against the economy and the banking sector," he told An-Nahar.
Washington has labelled Hezbollah a global terrorist group since 1995, accusing it of a long list of attacks including the bombing of the US Embassy and Marine barracks in Lebanon in 1983.
BLOM BANK director general Saad al-Azhari told reporters that no threats had been received by the bank ahead of Sunday's blast.
A civil defence official said one person had been lightly wounded in the attack.
There was confusion over where the bomb had been placed.
The National News Agency said it had been left under a car, but police chief General Ibrahim Basbous said it had been put in a plant pot.
The AFP correspondent saw damaged cars near the scene of the blast in the Verdun business district before an army patrol arrived and kept journalists back.
Twin bombings in the densely populated neighbourhood of Burj al-Barajneh in November last year killed 44 people. They were claimed by the Islamic State jihadist group.
Burj al-Barajneh is in the southern suburbs of Beirut, where the Hezbollah group holds sway.
Last year's twin bombings came after a string of attacks in 2013 and 2014 targeting the group by Sunni extremist factions which cited Hezbollah's military support for Syrian President Bashar al-Assad.