Proctor appealed his suspension, meaning he can pitch until a hearing is held and a ruling is issued.
Torre will miss Monday's game against the Mariners. Bench coach Don Mattingly will manage in Torre's absence.
The problems started after Josh Phelps slid hard into Mariners catcher Kenji Johjima. When Phelps came up again, Jarrod Washburn hit him in the back with the first pitch. At that point, the umpires warned both dugouts for the second time in three days.
Proctor then threw an inside pitch to Yuniesky Betancourt in the seventh. Betancourt pointed his bat toward the mound, catcher Wil Nieves grabbed him, and the benches and bullpens emptied. No punches were thrown.
Proctor and Torre were ejected.