The Rotherham-based peer appeared at Sheffield Crown Court on Monday for what was due to be the start of his trial.
But the Recorder of Sheffield, Judge Jeremy Richardson QC, said the trial could not go ahead due to Ahmed's QC being ill. The trial was rescheduled for July 13.
Ahmed, 61, is charged with a serious sexual assault against a boy under the age of 11 and the indecent assault of the same boy.
He is also charged with two counts of attempting to rape a girl who was under the age of 16.
All these charges relate to alleged incidents in the early 1970s.
Ahmed has pleaded not guilty to all counts.
The peer appeared under his name Nazir Ahmed along with two of his brothers.
One of these counts relates to when the boy was under eight, in the late 1960s.
Mohammed Tariq, 63, of Gerard Road, Rotherham, is charged with two counts of indecent assault against a boy under 11.
Farouq has pleaded not guilty to all the charges and Tariq has not entered any pleas.
Ahmed, of East Bawtry Road, Rotherham, stood in the dock with his brothers, wearing a dark suit. All three were given bail.
A further hearing in the case was scheduled for April 14.
Ahmed was made a life peer in 1998 and made regular appearances in the media, where he was often called on to comment on issues facing British Muslims.
He resigned from the Labour Party in 2013.