A spokesman for the Texas Department of Justice said that the state's stock of pentobarbital, the barbiturate used for the death penalty, has nearly run out.
The state will have to find an alternative whether "another provider for the pentobarbital, or other options that would involve other drugs besides pentobarbital," he said.
Pentobarbital is an anesthetic used to euthanize animals.
The spokesman said that two executions scheduled for September will take place and that a solution should be found by that time. He said the state plans to continue with lethal injections.
Texas has executed 503 people since the death penalty was reinstated in the US in 1976. A total of 1,342 people have been executed in the country since then.
Texas has already put to death 11 of the 22 people executed in the US in 2013, according to the Death Penalty Information Center.
Edited by Bonnie Malkin