Pugh was hurt after taking a hit to the head at Thursday's practice. He felt a headache Friday morning, Coughlin said.
"He's going through all the [concussion] protocol," Coughlin said. "So he'll be out until he passes all that protocol."
Pugh, 23, was selected by the Giants in the first round of the 2013 NFL draft out of Syracuse. He is currently behind starter David Diehl on the team's depth chart, but has been taking occasional snaps with the first team during training camp.
Also on the injury front, cornerback Corey Webster did not practice Friday due to a groin strain.
"[Corey and the medical staff] are going to do what they have to do to not turn that into something difficult," Coughlin said. "So he'll get some downtime to rehab."
Wide receiver Hakeem Nicks missed his second consecutive practice due to a groin injury.
Nicks downplayed the severity of the injury Friday, saying he wants to be careful following an injury-plagued 2012 season.
Coughlin was told by a team doctor that the 25-year-old could be back for Tuesday's practice.