In a court filing Sunday, her attorneys claim the misconduct was discovered during closed proceedings last week. They did not cite specifics but note that removing the juror would also be an option. That would leave five alternate jurors, in addition to the 12 who will decide the case.
Arias' lawyers argued last week the prosecutor committed misconduct by signing autographs and posing for pictures outside court.
The judge questioned jurors individually in private, then a legal correspondent for Turner Broadcasting's "In Session" was asked about what she saw.
Defense lawyers contend the prosecutor's antics may have tainted the jury if anyone on the panel witnessed it.
Testimony in the case is set to resume Tuesday.