The claim was made as Bhutto was buried in her ancestral village in the province of Sindh against a backdrop of continued violence, with the death toll from disturbances rising to 31.
Cheema also said Bhutto died from injuries caused by hitting her head on her car's sunroof as she came under fire, rather than from bullet wounds or shrapnel.
Contradicting the official account, a close Bhutto aide told the media on Saturday that she saw a bullet wound in the head when she bathed Bhutto's body after her assassination.
"I was actually part of the party which bathed her body before the funeral," said Sherry Rehman, who served as Bhutto's spokeswoman and who was in the motorcade at the time of the attack.
"There was a bullet wound I saw that went in from the back of her head and came out the other side.
"We could not even wash her properly because the wound was still seeping. She lost a huge amount of blood."
Rehman said: "The hospital was made to change its statement. They never gave a proper report. ...
"This is ridiculous, dangerous nonsense because it is a cover-up of what actually happened."
Earlier reports said Bhutto was gunned down by an assassin.
The assassin then blew himself up in an attack that killed a total of 16 people at the end of an election campaign rally in Rawalpindi on Thursday.
While pointing the finger at al-Qaeda, Cheema said Mehsud was also behind a suicide attack on a Bhutto rally in October that left 140 dead.
Pakistani authorities say Mehsud is based in the tribal region of South Waziristan.
'Pack of lies'
Cheema's claim that Bhutto's death was not caused by bullet wounds but by head injuries was described as "a pack of lies" by an aide of the slain politician.
Farooq Naik, a senior official in Bhutto's Pakistan People's Party (PPP), said: "Two bullets hit her, one in the abdomen and one in the head.
"It is an irreparable loss and they are turning it into a joke with such claims. The country is heading towards civil war."
Farhatullah Babar, a another PPP spokesman, said on Saturday: "The story that al-Qaeda or Baitullah Mehsud did it appears to us to be a planted story, an incorrect story, because they want to divert the attention."
He said Bhutto had earlier told the government of "elements" other than al-Qaeda that she thought could be a threat to her, but officials never investigated.
Kamal Hyder, Al Jazeera's Pakistan correspondent, said people were asking why the car in which Bhutto was travelling was not damaged by the fatal attack.
"A lot of people in Pakistan believe there may be some kind of conspiracy behind the assassination," he said.
Questions have also been raised as to why the scene of the attack that killed Bhutto was hosed down by the authorities soon after the blast, a move that may have destroyed valuable evidence.
Pervez Musharraf, the Pakistan president, called Asif Ali Zardari, Bhutto's husband, promising to make every effort to bring the attackers to justice, state-run Pakistan Television reported on Saturday.
And Nawaz Sharif, a former prime minister, led a 47-member delegation of other opposition leaders to meet Bhutto's family to express condolences, Sadiq ul-Farooq, a spokesman for Sharif's party, said on Saturday.
|Hundreds attended Bhutto's funeral at the|
family mausoleum at Larkana in Sindh
For his part, Zardari told BBC radio that Bhutto left instructions about the future of the PPP to be read in the event of her death, which would be made public on Sunday.
He said the couple's son would read out the message.
Zardari also revealed that Benazir had made detailed plans for her burial, including changing the location of the plot from his family's ancestral tomb to her family's mausoleum.
On Friday, hundreds of thousands of mourners gathered for Bhutto's funeral in front of the mausoleum in Garhi Khuda Bakhsh, a village 5km from the Bhutto home in the town of Naudero in Larkana district.
Supporters arrived by tractors, buses, cars and Jeeps that were parked in dusty fields surrounding the mausoleum - a vast, marble structure.
Bhutto had returned to Pakistan from Dubai in October, ending more than eight years of self-imposed exile after reaching an understanding with Musharraf.