Edwards' lawyers filed the motion Thursday afternoon and have asked for a 60-day extension.
The nature of the medical condition was put in a separate sealed document for Judge Catherine Eagles to review.
The government has responded by saying it is ready for trial, and oppose a continuance based on the need for more preparation. Prosecutors say they take no stand on the basis of a medical issue.
The trial was set to begin Jan. 30.
Edwards is accused of using about $1 million in undisclosed payments from campaign donors to cover up an affair during his 2008 White House bid. He has pleaded not guilty.
The 2004 Democratic vice presidential nominee had an affair with campaign videographer Rielle Hunter, eventually fathering a child. Prosecutors contend that Edwards used money from donors far in excess of legal campaign limits to keep the dalliance under wraps.
Much of the undisclosed money was funneled to Andrew Young, a close aide to Edwards who left the campaign and falsely claimed paternity of the senator's illegitimate child. Young and his wife invited the pregnant Hunter to live in their home near Chapel Hill and later travelled with her as tabloid reporters sought to expose the candidate's extramarital affair.
Edwards says he knew nothing of the checks, cash, and private jets used to fly Hunter across the country and put her up in luxury homes and hotels.
Edwards had just won a victory in court last week when Judge Eagles said she will consider allowing two former members of the Federal Election Commission to testify at his trial. They're expected to say thay what Edwards is accused of doing is not illegal. Eagles said she wants to hear the prosecution's case at Edwards' upcoming trial.
In October, Judge Eagles denied defense motions to throw out the case. Edwards' lawyers alleged the case was sought by a partisan Republican prosecutor bent on taking down a big-name Democrat. Edwards attorneys say the money for Hunter was a gift unrelated to campaign expenditures. They say that legally, donors can help pay for a candidate's personal expenses unrelated to campaign. They also said money from donors never went directly to Edwards - it was handled through third parties.
However, prosecutors say that if it was third party expenditure, Supreme Court rulings state that intent behind donations must be "unambiguously clear."