The lawsuit, which had been expected, was filed on the first anniversary of Jackson's death, just beating a one-year deadline for an action against the 'Thriller' singer's doctor.
Joseph Jackson, 80, alleges in the suit filed in federal court in Los Angeles that Murray was too slow to call emergency medical services for help, and he later made statements to authorities which turned out to be false, including that Murray was by Jackson's side monitoring his pulse.
The lawsuit states that after paramedics arrived at the Los Angeles mansion where Jackson suffered cardiac arrest, Murray failed to inform them the singer had been given the powerful anesthetic propofol, which he used as a sleep aid.
The suit claims that Murray later changed his story about what happened, and said that he only discovered Jackson was not breathing less than 20 minutes before paramedics were called.
"Defendant Murray's conduct of failing to call (emergency services), of leaving Michael Jackson's bedside, and conducting CPR on the bed instead of a hard surface was below the standard of medical care for physicians," the lawsuit states.
Authorities have ruled Jackson's death a homicide and said propofol was the key drug in Jackson's system that led to his death at age 50 on June 25, 2009, in Los Angeles.
Medical experts have said propofol should be administered in a hospital setting, and that it was highly unusual for Murray to give it to Jackson at his home.
In a statement, Murray's lawyer said, "We continue to maintain Dr Murray neither prescribed or administered anything that should have killed Michael Jackson...Dr Murray has not been found guilty of anything and we believe his innocence will be proven in a court of law."
Jackson's "polypharmacy"
But in his lawsuit, Joe Jackson contends Murray was "reckless" in administering a "polypharmacy" of different drugs to Jackson, "including propofol every night as a sleep aid."
It claims the singer was addicted to prescription drugs, and that Murray had a history of prescribing such drugs to Jackson dating to at least 2008.
California authorities have charged Murray with involuntary manslaughter in connection with Jackson's death and he faces up to four years in prison if convicted.
With that case ongoing, a state judge earlier this month allowed Murray to keep his California medical licence.
A civil lawsuit can run parallel to a criminal case, and its main purpose is to seek monetary damages.
The lawsuit, which was filed on behalf of Joe Jackson by attorney Brian Oxman, does not specify an amount of monetary damages that the pop star's father is seeking.
At the time of his death, Jackson was in the middle of rehearsals for a series of comeback concerts in London organized by AEG Live, a subsidiary of the Anschutz Company.
Joseph Jackson's lawsuit does not name AEG as a defendant, but the company has admitted hiring Murray to care for Jackson as he prepared for the concerts.
The lawsuit states that Joe Jackson "believes there are other parties responsible for Michael Jackson's death" and that he could amend his complaint to include those other parties.
The suit also named Joe Jackson's wife, Katherine Jackson, as a nominal party, but Adam Streisand, attorney for Katherine Jackson, said the move was highly unusual and unwelcome.
"The impression that Brian Oxman creates by doing this is that somehow Mrs Jackson...(is) a part of this action against Conrad Murray, and nothing could be further from the truth," Streisand said.