If the at-fault driver is insured then the bills will be paid by his insurance company, a Ministry of Health source said, according to the Saudi Gazette.
According to the report, the rules will apply to foreign drivers as well as Saudis.
More than 100 people are injured and around 23 killed every day on Saudi Arabia's roads, with an average of 1,460 accidents every day, the Saudi Gazette said, citing Directorate General of Traffic figures for 2015.
Doha-based insurance expert Roger Phillips of Pinsent Masons, the law firm behind Out-Law.com, said: "This is another example of the continuing change and development in the Saudi insurance markets. Motor claims are sensitive to many environmental factors and changes affecting motor insurance need careful planning and introduction, as the condition of and modernisation of the roads and transport systems can be a significant risk element for insurers in Saudi to factor in."
Moody's investors service said last year that Saudi Arabia's insurance market is the second-fastest growing in the Gulf Cooperation Council (GCC), with room for growth due to low penetration levels.
The GCC region is becoming a more attractive option for insurance, with new regulatory regimes and technological advances, according to Phillips.
Reports estimate that the insurance industry across the GCC will reach $37.5 billion by 2017, at an estimated compound annual growth rate of 18%, Phillips said in a recent look at the industry.