Mr Musharraf, who was the army chief during the Kargil War, also demanded that Mr Sharif should be tried for treason for his remarks on the 2008 Mumbai terror attack.
The 74-year-old retired general, facing a slew of cases in Pakistan, has been living in Dubai since last year when he was allowed to leave the country for medical treatment.
While reacting to Mr Sharif's statement on the Mumbai attack, Mr Musharraf, the chief of the All Pakistan Muslim League, also talked about the Kargil War, blaming withdrawal of the Pakistan Army on Mr Sharif.
Elaborating on the war and its happenings, he said that Pakistan was in a dominating position in five different fronts in the war, and that the then-prime minister was briefed on the situation at least two times.
He rejected Mr Sharif's claims that he was not taken into confidence about the withdrawal of the Pakistan Army from Kargil.
"He kept asking me whether we should withdraw," said Mr Musharraf in his video statement.
The former president and military ruler also said that then-senator Raja Zafarul Haq and interior minister of the time Chaudhry Shujaat had opposed the withdrawal of the army.
"He (Sharif) blamed the whole thing on me," the former army chief said.
On Mr Sharif's statement on the Mumbai terror attack, Mr Musharraf said that holding the Pakistani establishment and the army responsible was extremely disappointing.
In the message, Mr Musharraf derided Mr Sharif for his comments about Pakistan's involvement in the 2008 attacks which took the lives of 166 people, saying that Mr Sharif should be tried for treason under Article 6 of the Constitution for his comments.
He also called the former prime minister a "traitor" for defaming Pakistan Army and the establishment on the world stage.
The video message was released as a response to Mr Sharif's allegations about the involvement of "non-state actors" in the Mumbai attack.
Yesterday, Pakistan's National Security Committee had condemned Mr Sharif's statement as "fallacious" about the Mumbai terror attack and termed it as "incorrect and misleading".