The firm announced it made the decision due to the "wellbeing" of its workforce and those "within our extended network".
Sanctions imposed on Russia have heavily restricted the ability of companies to sell goods there.
JLR, based in Whitley, produces Jaguar cars and Land Rover and Range Rover sport utility vehicles.
The company said: "Jaguar Land Rover’s first priority is the wellbeing of our entire workforce and their families, as well as those within our extended network."
It adds: "The current global context also presents us with trading challenges so we are pausing the delivery of vehicles into the Russian market and continually monitoring the situation on behalf of our global customer base."
Meanwhile, BMW said its Mini plant in Oxford would see production stood down for five days from March 7 to 11 "as a result of the ongoing parts supply situation, now including the conflict in Ukraine".
The company said: "We are monitoring the situation very closely and are in constant communication with our associates and suppliers.”
A BMW spokesperson added: "No associate will have to go unpaid as a result of the stand down and we are in discussions with the union about how this will be managed.”
The plant also suspended production last week due to the global shortage of semiconductor chips.