During the Rangers' 11-4 win over the Red Sox on Sunday, Beltre, who was playing in his third game back off the disabled list from a left hamstring strain, ran from first to third on a single to left-center by David Murphy.
"It scared the [heck] out of everybody, including me," Washington said. "I yelled at him, 'What the [heck] are you doing?' He said, 'Playing baseball.' But he was fine."
Washington referred to his own hamstring issues during his 10-year playing career with five different teams in discussing how he will assess Beltre's strength level.
"I know what it feels like and how you can determine your confidence level," Washington said. "I'll lean on the trainers, but I will let him determine things for the most part."
Washington said he would have Beltre in the DH role on Monday and Wednesday of the three-game series against the Rays and at third base in Tuesday's contest. Beltre is hitting fifth in the lineup, but Washington expects him to move back into the cleanup role over time.
"He'll get it back together," Washington said.
Beltre, who missed 39 days, notched his 2,000th career hit with a line-drive single off Red Sox starter John Lackey in the sixth inning of Sunday's win.