Approximately 5,500 DOT employees are headquartered at the agency's Washington, D.C., office, which shares a Metro station with the Navy Yard.
Foxx said the agency's workforce was thinking about their counterparts at the Navy Yard that were affected by Monday's shooting.
"Our hearts go out to the families of those who died in this senseless tragedy and the victims who are recuperating from their injuries," Foxx wrote. "Our thoughts and prayers are also with the many people traumatized by this long and frightening ordeal."
Employees at the DOT were ordered to shelter in place until 3 p.m. on Monday at the Navy Yard while police searched for potential suspects in the shooting.
Foxx said on Tuesday that no one at the DOT was hurt in the incident. He also promised that the agency would operate normally on Tuesday.
"I'm also very grateful that no one at DOT Headquarters was hurt, and I'm proud of the professionalism that everyone at DOT showed by remaining calm and patient throughout the day," Foxx wrote. "We at DOT share with our Navy Yard colleagues a commitment to public service. Today, we will do our best to return to that commitment."