Robert A. Singer, 49, was arrested at his home on charges that he sent the images to a detective posing as a 33-year-old mother and her 12-year-old daughter, U.S. Attorney Michael Garcia said.
The museum, which closed in 2004 and plans to reopen in 2012 after renovations, said in a statement that officials were "horrified" by the events.
The museum said in its statement it had suspended Singer and barred him from the property.
"Anyone who does anything that might endanger the welfare of a child has no place here," it said. "Harming children is against everything we stand for as an organization and as individuals."
The images sent from Singer's museum computer depicted sexual acts between minors and adults, the complaint said. Singer also sent the daughter two images with instructions to "just delete it when you are done."
Singer also exchanged images with other people while sending the pornography to the detective in August and September, the complaint said.
Singer was charged with five counts of distributing child pornography in interstate commerce. If convicted, he could face a prison term of up to 40 years on the most serious charges.
A man who answered the phone at Singer's residence Tuesday said that there was no one to immediately comment on the arrest.