In a letter to families in the district, Washburn said the decision was made in compliance with Gov. Greg Abbott's order to close school statewide through the school year's end, which made made earlier in the day.
DSISD students will continue with virtual learning as the closures continue.
Washburn also said he and school officials will be in touch with seniors to brainstorm "meaningful ways we can honor this group in these unusual circumstances," including turning the Tiger Stadium lights on at 8:20 p.m. each Friday night as a signal of "appreciation, respect and gratitude for the class of 2020."
"This is not an easy announcement to make," Washburn wrote. "We miss being with our students every day to provide a personal and caring touch to their learning. However, their safety and well-being, as well as the safety and well-being of our staff and community, must be our highest priority."