Musharraf said he felt the aftershock of the explosion on Sunday as he drove away from the blast site in Rawalpindi, a military garrison city near Islamabad.
"It was certainly a terrorist act and certainly it was me who was targeted," Musharraf said on state-run PTV late on Sunday.
He said he had been returning from Chaklala air base in his motorcade when the explosion went off, cracking the bridge's concrete.
"I was going from Chaklala and we crossed the Ammar Chowk bridge and there was an explosion just one minute or half-a-minute after we crossed. It must have been a large explosive because it damaged the concrete and I felt the effect of the explosion in my car."
The Pakistani president, who has previously been targeted by would-be assassins in the southern city of Karachi, blamed "the militants, extremists and terrorists who are out to not only damage our nation but also bring a bad name to our great religion" for the attack.
"The internal danger comes from religious and sectarian extremists and this is a typical example of that. We have to guard against them. We have to fight these people with all our might," he said.
Musharraf has angered many groups with his support for the US-led campaign to oust the Taliban regime in neighbouring Afghanistan.
Three would-be assassins were sentenced to 10 years' hard labour for a Karachi incident in April last year, when a remote-controlled device failed to detonate an explosives-laden van near the president's motorcade.
Military spokesman Major General Shaukat Sultan also described Sunday's attack as an act of "terrorism".
Musharraf is a key supporter of
America's 'war on terror'
"It is clearly a terrorist act because an attempt has been to blow up the bridge," the general told AFP.
Witnesses said army and police ringed the site of the explosion after closing the bridge for traffic.
"We are determining what caused the explosion, but there were no casualties," city police chief Marwat Shah told AFP, adding that the explosion had damaged the bridge which leads to the city's military area.
General Musharraf came to power as head of the army in a bloodless coup in 1999.
He became a key ally of President George Bush during the attack on neighbouring Afghanistan in 2001, placing the country on the frontline of the Bush's so called "war on terror".
President Musharraf's position was a difficult one, finding himself caught between the need to support US plans to attack Afghanistan and prevent a public backlash and further radicalisation of Muslim groups at home.
He headed off the threat of mass protests by ordering a crackdown on several leading Islamic scholars and Islamist groups.
Dissident groups supporting al-Qaida have threatened to kill him for his cooperation in the "war on terror".