The Democratic congressman, who is seeking a fifth term, wasn't at the office when a staffer discovered the envelope, Grijalva spokesman Adam Sarvana said.
Authorities said it's not immediately known who sent the envelope to Grijalva, who has been threatened previously.
Sarvana said Grijalva was at another Tucson office Thursday — his campaign office — and was made aware of the envelope's discovery.
A Phoenix man was indicted in June for allegedly threatening to assault, kidnap and murder Grijalva and his aides. In July, a bullet was fired into Grijalva's Yuma district office shortly after he reversed his call for a convention boycott because of Arizona's new immigration law.
The Arizona law would require police enforcing other laws to question people about their immigration status if there's reason to suspect they're in the United States illegally. It was to go into effect this summer, but a judge put on hold key provisions pending the resolution of a legal challenge.