The woman is suspected of falsely reporting her car stolen shortly after the accident in order to protect her son from criminal charges.
The victims, aged 31 and 32, were cycling home from Walpurgis Night celebrations when they were hit by a car travelling at high speed at around 10pm on Monday. Both died at the scene.
The car was later found not far from where the accident took place.
The 23-year-old driver fled the scene but was apprehended by police on Tuesday morning.
“He was arrested calmly in his home outside Karlstad,” said Värmland police spokesman Thore Persson.
The man is suspected of having driven the car under the influence of alcohol.
A 22-year-old passenger is also suspected of drunk driving and driving without a licence having taken control of the steering wheel when the driver was injured in the collision with the cyclists.