The crew carrying 60-year-old blood-clot patient Glenn Buscombe stopped on the A38 near Carkeel roundabout in Cornwall to pick up the woman and man.
Confirming what happened, South Western Ambulance Service said it was because the pair were on  a "dangerous" road and they were "doing the right thing".
Mr Buscombe has since made an official complaint to the ambulance service.
The vehicle had been taking the patient from his home in Polperro to Derriford Hospital in Plymouth.
Mr Buscombe said: "My wife called the doctor because my right leg was really swollen and I was in a lot of pain."
He said he was "pretty shocked" when the ambulance pulled up to pick up the hitch-hikers.
"I said to the paramedic 'What's going on?' And he said he did not know what the driver was playing at."
Mr Buscombe added: "I would be the first to pick up a damsel in distress but it was an emergency.
"I made the complaint because someone else could be in a more serious condition."
An ambulance service spokesman said the crew "thought they had a duty of care to the couple because the road is pretty dangerous".
He added that the ambulance was not on an emergency run, but had been asked by a doctor to take Mr Buscombe to the hospital for treatment to a blood clot.
The couple were dropped off at a service station about a mile down the road .
"The driver thought, 'Do I leave them or do I drop them off at a safer place?'," the spokesman said.
"The journey was 1.2 miles and added maybe a couple of minutes extra to the journey.
"They were just doing the right thing."
The ambulance trust said in a statement: "The trust has received a complaint from Mr Buscombe relating to a routine transfer from his home address to Derriford Hospital, Plymouth, in the early hours of Sunday, April 6.
"The trust takes all complaints seriously and has started an investigation to establish exactly what happened during the transfer."
Debbie Pritchard, chief executive of Healthwatch Cornwall, said: "We would be saddened to learn the ambulance crew did this while transporting a patient and hope the investigations taking place will be thorough.
"We hope the gentleman concerned in this instance is recovering well and he receives a response very soon."
An ambulance crew taking a man to hospital stopped to pick up two hitch-hikers on route.