Judge Steven Taylor said the man was hospitalized and is expected to fully recover. His notes were destroyed, and the judge said reporters should not contact him.
A female alternate took his place, leaving two other alternates. Court rules prohibit identifying jurors.
The jury now has six women and six men, and the defense was set to begin its case in the April 19, 1995, bombing of the Alfred P. Murrah Federal Building, which killed 168 people.
Prosecutors, who are seeking the death penalty, rested their case Friday after questioning 151 witnesses and introducing more than 1,000 pieces of evidence over 29 days.
Word of the heart attack followed a ruling by the judge that defense attorneys can test unidentified fingerprints in a bid to show Nichols took the blame for others who aided in the bombing.
The defense is hoping to match fingerprints found in Timothy McVeigh's (search) car and a hotel room where he stayed days before the bombing to a gang of white-separatist bank robbers.
Defense attorneys allege the robbers helped McVeigh plan the bombing and will suggest a wider conspiracy during their case.
The trial was supposed to have six alternates, but two jurors and one alternate were dismissed before the start of trial after the state revealed they were distant relatives of an assistant Oklahoma County district attorney. The district attorney's office is prosecuting the case.
Prosecutors did not reveal the family ties until after the close of jury selection, drawing criticism from Taylor. He said if he ran out of alternates, he would dismiss the case.
Defense attorneys allege that McVeigh received substantial help from others and that Nichols was set up to take the blame for the bombing.
Dozens of people in Oklahoma and elsewhere reported seeing a second person who did not resemble Nichols with McVeigh in the days and weeks prior to the bombing.
Evidence concerning the enigmatic suspect, known as John Doe No. 2, will be presented.
Defense attorneys plan to question FBI artist Raymond Rozycki, who drew a sketch depicting the muscular, dark-skinned suspect based on a witness description.
The day after the bombing, a worker at a Ryder truck leasing agency in Junction City, Kan., where the truck that delivered the bomb was rented, told authorities that McVeigh was accompanied to the agency a heavy, well-built man with brown eyes and hair.
The employee, Tom Kessinger, said the man wore a black T-shirt and had a tattoo on his left arm. He wore a baseball cap with white and blue zigzag patterns.
Defense attorneys had planned to question up to 800 witnesses, but the defense witness list was pared down after the judge ruled there was no evidence McVeigh received help from anyone else in the bombing. The ruling limited defense attorneys' ability to explore evidence of alternative suspects.
About 200 witnesses remain on the defense witness list. Defense attorneys expect to question them over the next three weeks.
Nichols, 49, is serving a life prison sentence following his 1997 convictions on federal involuntary manslaughter and conspiracy charges in the deaths of eight law enforcement officers in the bombing.
In Oklahoma, Nichols is charged with 161 counts of first-degree murder for the deaths of the other 160 victims and one victim's fetus.
McVeigh was convicted on federal murder charges and executed in 2001.