The pair were about an hour north of Alice Springs on the Stuart Highway on Wednesday afternoon when the man, whose age was not given, was killed.
“It is believed that two French tourists, being husband and wife, were at a rest stop 30 kilometres (18 miles) south of the Aileron Roadhouse when they were approached by an unknown man,” said Detective Superintendent Travis Wurst.
“The man has allegedly then stabbed the male tourist to the neck, in an unprovoked attack. The male passed away at the scene.”
The attacker fled in a vehicle which was stopped soon after by police with the man running off into bushland. He was arrested on Thursday morning.
Police said the wife was being treated for shock at Alice Springs Hospital.
The Stuart Highway, a popular tourist drive, is the principal north-south route through Australia's remote central interior, spanning nearly 3,000 kilometres from Darwin via Alice Springs to Port Augusta.