The government of President Nicolas Maduro in February kicked out three consular officers on charges they were recruiting students to participate in anti-government protests that have sparked the country's deadliest unrest in a decade.
The State Department denied those accusations.
The embassy said that because of the expulsions and the delays in approval to bring in new consular officers, it no longer has sufficient staff to process first-time tourist visa requests.
"Until further notice, we are able to offer such appointments only in emergency situations," the embassy said in a statement posted on its website.
It said it will still process visa renewals and applications for other types of visas, and that it will attend to those who already have appointments.
The statement encouraged those who already have appointments not to miss them "because it is unlikely under current staffing conditions that we will be able to re-schedule your interview in a timely manner."
The two countries have not had ambassadors in each other's capitals since late socialist leader Hugo Chavez expelled the US envoy to the OPEC nation in 2008.
Anti-government protests have convulsed the country since the middle of February and left at least 34 dead.