Grodzki added that the package, addressed to him, was sent by mail and was checked by Senate’s security.
Warsaw police department said on Saturday it was already investigating the case.
Earlier this month, Justice Minister Zbigniew Ziobro said prosecutors in Poland will investigate death threats sent to some politicians, including opposition leader Donald Tusk.
On November 1 Tusk, a former prime minister, published a short video on Twitter in which he described a letter containing death threats.
Similar letters were sent that day to a number of other major opposition politicians and journalists, Poland's PAP news agency reported.
Tusk said in the video that the letter was sent to him on what would have been the 56th birthday of Paweł Adamowicz, the mayor of the northern Polish city of Gdańsk who died in 2019 from severe wounds inflicted by a knife-wielding attacker during a high-profile charity event.
“I'll put a combat knife in your stomach, just like Stefan Wilmont did to … Adamowicz,” the letter said, according to Tusk.
He condemned the threats as part of “a wave of hatred, contempt and violence on the rise in Poland,” for which he blamed the leader of the ruling conservative Law and Justice (PiS) party, Jarosław Kaczyński.
“You are directly responsible for this as the head of the ruling camp and as the deputy prime minister for security matters,” Tusk said in the video, addressing Kaczyński.