The victims, both 24 years old, were on top of a tank at the time of the explosion, KTVT-TV, Fort Worth, reported.
Van Zandt County Fire Marshal Chuck Allen said the man received burns to his face, chest and arms, while the woman suffered life-threatening injuries.
Another of the five tanks at the storage facility near Van, about 70 miles east of Dallas, exploded later.
Firefighters from Van, Grand Saline, Tyler and Lindale sprayed foam to prevent the fire from spreading to the other tanks.
The victims had not been identified, but were not believed to be employees of the facility, WFAA-TV, Dallas, reported.
They were transported to Parkland Memorial Hospital in Dallas, KTRK-TV, Houston, reported.