The suspect, 37, had a prior relationship with the victim, authorities said.
The five fragments are part of a 16-piece Dead Sea Scrolls collection at the Washington, D.C., museum.
The accusations made by the leader of Saudi Arabia's regional rival could further inflame the diplomatic crisis over the killing of the regime critic.
The U.S. National Hurricane Center warned Willa is likely to bring "life-threatening storm surge, wind and rainfall" to parts of west-central and southwestern Mexico.
The 88-year-old business investor and Holocaust survivor has been a frequent target for his left-leaning political involvement.