Beckham looks set to miss England's vital qualifiers with Israel and Russia at Wembley on September 8 and 12 unless the scan brings good news.
Beckham said: "At the moment, we're calling it a ligament strain, but I'm going for a scan to see exactly what it is and how long I'm going to be out.
"But at the moment, it doesn't feel great.
"This is an injury that takes four to six weeks, but who knows, if the scan is not so bad maybe I've got a chance to play (for England)."
Beckham suffered the injury in the 31st minute as both he and Pachuca's Fernando Salazar simultaneously made strong contact with the ball.
He looked to have jarred his right knee and rolled on the ground in obvious pain. He slowly stood up and motioned to the bench before limping off the field.
Galaxy physio Ivan Pierra helped the 32-year-old back to the Galaxy bench while coach Frank Yallop sent on Alan Gordon as a replacement.
The former England captain revealed that a desire to protect his ankle, which until recently had kept him out of action, had caused him to go into the tackle differently to when fully fit.
"I went into the tackle a little light because of my ankle and tried to compensate for that," he said.
"I'd have been better off not doing it at all."