"He was immediately isolated, as were two potential close contacts, and we are currently working with the league's chief medical officer," the Giants said in a statement.
Quest Diagnostics Training Center, the team's East Rutherford, N.J., practice facility, will remain open, and the Giants plan to practice and have meetings Friday.
DeGuglielmo is the third Giants coach this year to test positive for COVID-19. Offensive coordinator Jason Garrett and offensive assistant Stephen Brown missed the Giants' Dec. 20 game against the Cleveland Browns after they tested positive.
The Giants host the Dallas Cowboys at 1 p.m. EST Sunday in East Rutherford, N.J. Giants assistant offensive line coach Ben Wilkerson will fill in for DeGuglielmo.
The Browns on Friday also announced that their latest round of COVID-19 testing produced no positive results and they have received approval from the league to have practice Friday afternoon.
The team has placed more than 10 players on the reserve/COVID-19 list since Saturday. At least five Browns players are expected to miss the team's game on Sunday due to positive COVID-19 test results.
The Browns host the Pittsburgh Steelers at 1 p.m. EST Sunday in Cleveland. They can clinch a playoff berth with a victory.
The NFL announced Tuesday that tests found 21 new confirmed positive cases of COVID-19 cases among players and 37 among other personnel from Dec. 20 through Saturday.
A total of 618 positive COVID-19 test results -- 222 from players and 396 other personnel -- emerged from Aug. 1 through Saturday.