Taking suo motu cognisance from newspaper reports on the strike, a division bench of Chief Justice Prakash Tatia and Justice Jaya Roy also directed serving of notice on the union.
The Central Government Hospital Workers Union has called the strike to press for demands, including change in recruitment rules.
Secretary of the employees union, Abdul Kalam said, "24 employees have died over the year but their kin have not been given jobs."
Time-bound promotions have been pending since 2008, which should be cleared immediately, he said.