Interior Ministry officials said they had no information on the matter. Security officials said they were checking the report.
Turabi, who once organised an international Islamist alliance, was jailed and his opposition Popular Congress Party (PCP) banned after the government accused them of an alleged coup attempt last March.
The family said in a statement that his own physicians had said such an injection could harm 73-year-old Turabi.
"On Thursday April 14, 2005, four security staff, one posing as a vaccination functionary, injected Turabi with what security claimed was a vaccination against meningitis," the family said.
"Turabi's doctors, all of whom are known to security, were not consulted and none of them ordered this vaccination."
His family said they have been trying to secure his transfer to an independent hospital.
"It has been 22 hours since the injection and the exact health condition of Turabi is not known and is presumed to be in danger," it said.
Sudan's Attorney-General Mohamed Farid said on Thursday 24 people, mostly army personnel, had been convicted of waging war against the state by attempting the coup last March, adding two-thirds of those convicted were from the PCP.
Turabi was previously detained for more than two years following a power struggle with President Omar Hassan al-Bashir in 2001. But Sudanese officials say he will be released when Sudan's state of emergency is lifted in the capital, which should happen once a new government sworn in.
The signing of a peace deal in January to end more than 2 decades of civil war in Sudan's south will lead to the new government of national unity, expected to be formed by July.