It is understood the couple, who are aged in their 60s, may have run through a red light at the junction of Shands Road and Blakes Road in Prebbleton.
They died at the scene of the accident.
A Foreign Office spokesman said: “We are assisting the family of two British nationals following their death in New Zealand.
“Our staff are in contact with New Zealand police.”
Paul Lally, who lives next to the Shands-Blakes intersection, heard the crash and called emergency services.
The couple had arrived in the city of Auckland a week ago.
Inspector Peter Cooper, Canterbury rural area commander, said: “We’ve got some inquiries to do with the rental company just to ascertain who [the victims] are and we’ll try and let their next of kin know in England as soon as we can.
“This is a controlled intersection with a stop sign.
“There are a number of these in the Selwyn area and we want to go through, make sure we’ve got all the details … before we make any assumptions to the cause.”
Mr Cooper added: “Selwyn’s notorious for its number of intersections and the cross-traffic issues that we have because of that.
“It’s a… timely and unfortunate reminder of how you have to be careful at intersections.”
It is understood the intersection is due to be upgraded to a roundabout next year as the Shands Road and Blakes Road intersection was ranked 15th most dangerous in Canterbury over the past five years, with one person killed and two seriously injured in three crashes during that time.