The first hospital in Kuwait to enforce the new policy on only treating expatriates in the afternoon began the system on Sunday.
Jahra Hospital, to the west of Kuwait City, will carry out a six-month trial to see how the system works after it was voted into effect by MPs earlier this year.
If it is deemed a success then the Ministry of Health says that it will be extended to encompass all public health facilities.
The decision was made after complaints from Kuwaiti nationals stating that they faced long queues at hospitals and clinics due to the large volume of expats seeking treatment.
More than half of the country's population is made up of expats, who are drawn to Kuwait due to the high level of pay offered to take up positions within businesses.
Medical services are free to Kuwaitis while expats are charged an annual fee of $175 (£115) as well as an extra charge for procedures such as x-rays.
Under the new policy, nationals are given priority in the morning while expats can only seek medical attention in the afternoon, unless it is an emergency.
It means that expats are given less time to consult a doctor or medical professional and has led to some complaints that the system is racist.
Mohammad Abdulqader Al-Jassem, writer and lawyer, turned to Twitter to suggest that the move amounts to racial segregation.
Medical care is not the first area to undergo such a change, as a number of governmental agencies in Kuwait operate a similar system.
The traffic department, for example, only deals with applications from nationals in the morning and expats in the afternoon.
Kuwait has recently started to change some of its policies towards expats in a bid to cut down on the country's reliance on foreigners, giving its citizens a better chance of securing the top jobs.
There is talk of introducing income tax, which would impact on the wages and affordability of life for those living in the oil-rich state.