The state TV headquarters, the international airport and a military base in the city were all targeted.
The information minister said the situation was now under control and about 46 attackers had been killed.
Meanwhile, the army has also clashed with unknown gunmen on the outskirts of Lubumbashi, a military spokesman said.
He told the BBC that some of the attackers in Lubumbashi, the main city of DR Congo's southern mineral-rich Katanga province, had been arrested.
President Joseph Kabila, who won his second term in office two years ago, is touring Katanga but was not under any threat, DR Congo's Information Minister Lambert Mende told the BBC.
Mr Mende said the attackers at the state TV and radio headquarters had been armed with weapons such as knives, and there was "no chance of them even to maintain their positions, even for a single hour".
"People were frightened when security personnel were firing against these attackers," the minister told the BBC's Focus on Africa radio programme after visiting the RTNC headquarters.
He said the attackers numbered fewer than 100 and that the security forces had killed about 46 of them and captured about 10.
On the government's side, an army colonel was killed when the attackers struck the military base, Mr Mende told the BBC.
He said he understood that two staff members forced to read a statement on TV were safe.
Reuters said the statement appeared to be a political message against President Kabila's government.
"Gideon Mukungubila has come to free you from the slavery of the Rwandan," said the message, according to Reuters.
In 1997, Rwandan-backed troops ousted DR Congo's long-serving ruler Mobutu Sese Seko and installed Laurent Kabila - the father of incumbent leader Joseph Kabila - as president.
According to Reuters, Gideon is the nickname used for religious leader Paul Joseph Mukungubila by his followers. He ran unsuccessfully for president in 2006.
Mr Mende told the BBC the shooting in Lubumbashi was linked to a disarmament programme and not to the attacks in the capital.
The armed youths stormed the studio in Kinshasa around 08:40 local time (07:40 GMT) during a live magazine programme, shouting slogans - one of which in French said "for the liberation of Congo".
In a separate incident, a taxi driver told AFP that he had heard about "six or seven shots" from heavy weapons fired at the Tshatshi military camp. The shots were heard between 09:00 and 09:30 local time.
After RTNC went off air, a customs official at Ndjili airport told Reuters: "Shooting has started here. They are shooting everywhere. We are all hiding."
Kinshasa RTNC TV has now resumed normal programming.
The US embassy in Kinshasa has advised all US citizens not to travel around the city until further notice.
"The embassy has received multiple reports of armed engagements and fighting around Kinshasa… The embassy has also received reports that there are police and military checkpoints and barricades in many places,"