The Brit, fresh from winning the men's singles gold medal at the Rio Olympics, eased to a 6-3 6-2 victory in Cincinnati on Wednesday.
But Murray needed treatment on his right shoulder during the win, which was still comprehensive despite the injury worry.
The two-time champion and top seed required just one break in the first set before rolling out to a 5-1 lead in the second.
Murray crushed the Argentinean on his way to gold in Rio, and he made it five wins in seven meetings with Monaco.
He finished with 15 winners and 17 unforced errors, completing victory in one hour and 17 minutes.
Next up for Murray is Kevin Anderson after the South African upset French 13th seed Richard Gasquet.