Separatist rebels in Manipur ordered all pharmaceutical companies operating in the state to pay militants a total of 10 million rupees (250,000 dollars).
The extortion demand was telephoned in to local newspapers in Manipur in early August and appeared as news reports.
The reports did not specify in detail who made the extortion demand, gave no deadline for payment and did not specify the consequences if no money was paid.
However, the state's top health official said the government was taking the demand seriously and was working with drug companies to encourage them to resume supplying Manipur.
"We're negotiating with companies to resume supplies very soon and have assured them of full protection and security," Manipur Health Minister Parijat Singh told AFP by telephone from state capital Imphal.
"There's no need to panic and in a day or two we shall ensure supplies of drugs," he said.
Among the thousands affected as drugs became scarce were many people living with AIDS in a region where HIV-infection rates are high.
"I have been without ART (anti-retroviral therapy) for the last four days -- there are no medicines available," Bimla, an HIV-positive woman, told AFP.
Pharmacy stores reported they were running low on many drugs and basic materials like syringes and bandages.
"It has been more than 10 days since the companies have stopped supplying medicines to Manipur," said S. Singh, a chemist in Imphal.
"Stocks of almost all life-saving drugs have dried up."
Police said they were investigating the extortion threat.
"No one has lodged a formal complaint... But we're acting on our own," said senior police official Clay Khongsai.
Local pharmaceutical firm representatives said they dared not approach the police or resume supplying the market.
"Militants in Manipur are capable of doing anything," said one frightened wholesaler, who asked not to be identified. "No one is willing to take the risk."
Manipur is home to about 19 rebel groups with demands ranging from independence to greater autonomy, but police said it was unclear which group was behind the extortion demand.