Police said one rocket smashed through a window of the building and injured people inside, a second exploded against a wall leaving while a third exploded on the pavement, damaging two cars.
The building hit by the rockets houses the offices of several companies, two restaurants and the headquarters of a charity foundation run by Saudi billionaire Al-Walid bin Talal.
A Lebanese police officer said: "Unknown assailants fired on Sunday at 2325 GMT three rockets from an assault rifle ... towards a building near UN House.
"Six civilians were slightly wounded by one of the rockets which exploded against a building next to the UN offices."
It was the third security breach in Beirut in the last 10 days, following two hand-grenade attacks which earlier targeted police stations without causing casualties.
Sunday's attack was the first to target the Lebanese capital's central area where tight security has been in place since the February 2005 massive car bombing that killed Rafiq al-Hariri, a popular former prime minister.
The area houses the sand-bagged UN House, the prime minister's offices and foreign diplomatic missions.
The Italian navy has meanwhile handed over to German command the UN naval force tasked with patrolling Lebanon's coastline to prevent arms smuggling following Israel's war with Hezbollah.
The ceremony on Sunday was also attended by major general Alain Pellegrini, United Nations interim forces commander in Lebanon who hailed the Italians' mission, which helped end a crippling Israeli blockade of Lebanon, as "a real success".
Germany has agreed to send up to 2,400 military personnel to Lebanon in the country's first mission in the Middle East since World War II.
Although Germany has sent a maritime fleet to Lebanon, having UN troops on the ground is a more sensitive issue because of the potential of conflict with Israeli troops.