The attack on June 2 killed six people, all of them Pakistanis.
Yazid claimed al-Qaeda's responsibility for the attack soon after the blast in a posting on a website.
It was unclear from what Yazid said, whether the embassy bomber was a Saudi, as many non-Saudis have settled in Mecca, or whether he had been recruited while visiting the city.
Yazid said the bomber had come to join a "jihad" in Indian Kashmir or Afghanistan, and became enraged by the publication of caricatures of the Prophet Mohammad in Danish newspapers in 2005.
The interview with Geo TV was said to have been conducted at an undisclosed location in Khost, Afghanistan, by Geo TV's reporter Najib Ahmad a few days ago.
This is the first independent media interview given by a well-known al-Qaeda member since May 2002, when two figures from the September 11 attacks, Khalid Sheik Mohammed and Ramzi bin al-Shibh, were questioned by Al Jazeera.
'Anti-Muslim credentials'
Replying to a question from Geo TV about Al-Qaeda's targets, Yazid said al-Qaeda had reached a point where they "see no difference between the [US] state and American people".
"The United States is a non-Muslim state bent on the destruction of Muslims. It is the American people who have voted George bush into power, knowing full well his anti-Muslim credentials," Geo TV quoted the al-Qaeda commander as saying.
"We have even destroyed US helicopters in Khost, Jalalabad and Helmand - reports of which have been carried by media worldwide.
"The mujahideen are hopeful and high-spirited. They are now expanding their areas of operations and carrying out actions in northern provinces too," he said.
Yazid, an Egyptian, served time in prison with Ayman al-Zawahri, the deputy al-Qaeda leader, following arrests after the assassination of Anwar Sadat, the Egyptian president, in 1981.
He is now allegedly commander of operations in Afghanistan and has been referred to as al-Qaeda's third most senior figure.
'Financial manager'
Earlier, the September 11 Commission, investigating attacks on the United States on September 11, 2001, described Yazid as the network's "chief financial manager".
During the interview, Yazid openly acknowledged al-Qaeda's responsibility for the September 11, attacks and berated the the government of Pervez Musharraf, Pakistan's president, for subsequently "betraying" the Islamist cause by siding with the United States.
Yazid defended the tactic of using suicide attacks and was unapologetic about the fact that the attack on the embassy killed Pakistanis, including one security guard on the gate and two policemen.
But the Egyptian said that al-Qaeda was not to blame for any of the bomb attacks in Pakistan late last year that targeted mosques.
Yazid is also known as Sheikh Saeed.