Byram scored two goals on four shots on net while adding two hits and a plus-4 rating in Tuesday's 7-3 win over the Red Wings.
Byram, who is dealing with an illness, was acquired by the Sabres from the Avalanche on Wednesday in exchange for Casey Mittelstadt, according to Elliotte Friedman of Sportsnet.
Byram missed Wednesday's morning skate due to an illness and is considered questionable for the evening's matchup with the Red Wings, Marc Moser of Altitude Sports 950 reports.
Byram had an assist, one shot and one hit in Saturday's 4-3 loss to the Maple Leafs.
Byram had two assists, two shots on net and one blocked shot in Sunday's 4-3 win over the Coyotes.
Byram logged two assists, two shots on net, one block and one hit over 18:42 of ice time in Tuesday's 6-3 win over Washington.
Byram had one shot on net, one block and one hit over 19:16 of ice time in Wednesday's 6-2 loss to the Capitals.
Coach Jared Bednar said Friday that Byram (lower body) will miss between a week and two weeks, Evan Rawal of Colorado Hockey Now reports. "He's going to miss a handful of games here," the coach said. "Lower body. Not serious at this point, so 7-10-14 days, some place in there. We put him on the IR today, so he's going to miss at least seven."
Byram (lower body) is being evaluated but has been ruled out for Saturday's game versus Florida, coach Jared Bednar told Evan Rawal of Colorado Hockey Now on Friday.
Byram recorded an assist, one shot on goal, one blocked shot and five hits over 19:26 of ice time in Wednesday's 5-4 overtime loss to Arizona.