According to German newspaper Bild, Djourou and Behrami came to blows in Hamburg's dressing room on Saturday, with Peter Knabel's men trailing 1-0 and on their way to a fourth straight defeat.
Hamburg went on to lose 2-0 - with Djourou sent off in the 88th minute - and they finished the weekend in last position in the Bundesliga standings, one point adrift of 17th-placed Stuttgart, who defeated Werder Bremen 3-2 on Sunday to rise off the bottom.
While Hamburg sporting director Dietmar Beiersdorfer confirmed there was an incident, he declined to give details and seemed keen to move on.
"There was an emotional dispute. It was discussed. It is regulated. Whoever breaks discipline must be punished," Beiersdorfer told Bild.
It is expected the two Switzerland internationals will be fined.
Hamburg are the only club to have played in every season of the Bundesliga and had to survive a promotion-relegation play-off with Greuther Furth to maintain their top-flight status last term.
If they finish in the bottom two positions this season, Hamburg will be automatically relegated.
After Saturday's loss, Hamburg captain Heiko Westermann conceded his team's second-half display was "not Bundesliga worthy", while midfielder Lewis Holtby was filmed angrily confronting the club's fans, seemingly frustrated at allegations he was not trying.
"I spoke to our fans after the final whistle, it was very emotional," he told Hamburg's website.
"I can understand that they are gutted but we have to stick together and not go our separate ways.
"I am the last person here who wants to be relegated with such a tradition-steeped club. The whole team doesn't want to."
Hamburg will travel to ninth-placed Werder Bremen on Sunday and host Augsburg, who sit sixth, the week after.
Those matches will be followed by three consecutive fixtures against fellow bottom-six clubs - Mainz, Freiburg and Stuttgart - before a clash with Schalke on the final day of the season.
"There are still a lot of points left to fight for, and we will be playing teams close to us in the table again, all of this gives me reason to hope," Holtby said.
