The state government and Allahabad's chief medical officer have been asked to come up with their replies on Thursday.
Justices Pankaj Mithal and Yashwant Varma passed the order on a plea filed by the All India People's Front and law student Vinayak Misra.
Their PIL follows the recent death in Noida of a pregnant woman who was allegedly denied admission at several hospitals. The PIL also called for a probe in that case.
The counsel for the petitioners argued that patients suffering from ailments other than COVID-19 should be treated at hospitals as they were before the coronavirus pandemic.
They asked the court to strike down the state government notifications which restrict government and private hospitals from offering treatment to non-COVID-19 patients.
They said the state government should create a separate set-up to treat COVID-19 patients and ensure that hospitals take care of people suffering from all ailments. CORR RAJ ASH ASH