Among the list of concerns were whether Le Pen is "in a unsafe state from the standpoint of psychiatry or forensic science".
Later on Thursday, she told reporters she felt "persecuted" and vowed not to attend the psychiatric evaluation.
Le Pen photographed and tweeted out the order with the words: "It's really incredible".
"I thought I had experienced everything: well no!"
Le Pen's ordeal started when a television journalist drew comparisons between Islamic extremists and far right politicians. "How far will they go?!"
According to a copy of the court order, which Le Pen posted to Twitter on Thursday, the judge wants the evaluation to assess if she suffers from any mental illness and if that could have affected her understanding of what she was doing when she posted the tweets. "I will wait to see how the magistrate intends to force me", she said.
But there were howls of indignation from Le Pen's supporters and allies nonetheless. Italy's Interior Minister Matteo Salvini said in a statement.
Her leftist nemesis Jean-Luc Melenchon, the France Unbowed leader who once called Le Pen "half-demented", tweeted his "total disagreement" with the court order.
Le Pen, who is head of the former National Front party - now National Rally (Rassemblement National) revealed on Twitter her shock and anger at being ordered to undertake a psychiatric assessment. "She is a political personality but this is not a political decision".
The charges stem from Le Pen's decision to post the images, including a photo of decapitated USA journalist James Foley, after the Paris terror attacks in November 2015.
"A court orders a psychiatric assessment for Marine Le Pen".
Le Pen later deleted the tweet with Foley's body after his family requested the removal.
If convicted, the politician faces a maximum punishment of a €75,000 fine and up to three years in prison.
Another National Rally lawmaker, lawyer Gilbert Collard, has also been charged for tweeting pictures of IS atrocities.
Last week, she repeated warnings that her party's existence was at stake if it didn't manage to win back two million euros in subsidies seized as part of an inquiry into claims it misused millions worth of European Parliament funds.