The suspect is identified as James Von Brunn who reportedly is active in the white supremacist movement.
The shooter was wounded and a security guard was killed during the shootout.
The shooting started on Wednesday afternoon when the gunman walked into the crowded museum and opened fire.
The suspected gunman is a racist, anti-Semitic Web site called the Holy Western Empire.
Von Brunn was convicted of attempting to kidnap members of the Federal Reserve Board in 1983.
The suspect is also the author of a book entitled, "Kill the Best Gentile."
Officials at the Illinois Holocaust Museum reacted to the tragedy on Wednesday afternoon.
The Illinois Holocaust Museum in Skokie is only seven weeks old. It has state of the art security but now that security has been heightened because of the tragedy in Washington.
"Shocked and sadden to learn of the tragedy today at the U.S. Holocaust Memorial Museum in Washington, D.C. Our prayers go out for a full recovery for the guard injured in the senseless attack," said Richard Hirschhaut, Illinois Holocaust Museum.
Officials say the constant safety of museum patrons is their top priority.
The museum was built with a state of the art security system which was developed in consultation with experts in the security field and with the support of the United States Department of Homeland Security.
In response to the tragedy in Washington, the museum has increased security in and around their property.
"The museum is working closely with the Skokie police department and other law enforcement agencies to ensure a heightened level of security in and around the facility," said Hirschhaut.
The alleged gunman who exchanged fire with security guards today has been identified as 88-year-old James Von Brunn, a navy captain in World War II with ties to a number of white supremacy groups.
"It's certainly not surprising that the alleged perpetrator of this senseless act would have been an adherent of white supremacy ideology. It makes this tragedy no less disturbing or shocking but is certainly a reminder to all of America that extremists hate and its potential for violence is very, very real," said Hirschhaut.
Museum officials say that this is a sad day for all. However, they say that the Illinois Holocaust Museum is a really safe place to come and visit and they are encouraging everyone to come and see the museum.