Florida Senator Marco Rubio said the rap star was unwise to pretend to shoot a clown dressed as the US president in the video.
Mr Rubio told TMZ: "If the wrong person sees that and gets the wrong idea, you could have a real problem."
The video, featuring Snoop Dogg and Kaytranada, is a remix of Lavender by Canadian group BadBadNotGood.
Mr Rubio added: "Snoop shouldn't have done that.
"We've had presidents assassinated before... so anything like that is something people should be really careful about."
The video shows Snoop shooting the Trump character with a gun that releases a flag with the word "bang" written on it.
Mr Rubio ran to be the Republican presidential candidate. He lost the Republican primary in his home state to Mr Trump.
Follow us on Facebook, on Twitter @BBCNewsEnts, or on Instagram at bbcnewsents. If you have a story suggestion email entertainment.news@bbc.co.uk.
Snoop Dogg has been criticised for shooting a toy gun at a Donald Trump character in a music video.