The company said staff who walk out in the ongoing dispute over the role of conductors would be paid the money when industrial action came to an end.
The RMT union described it as "another outrageous and bullying attack on staff fighting for public safety".
General secretary Mick Cash said staff were "signing away basic human rights".
Passengers on Southern services have suffered months of delays and disruption caused by the industrial action over the introduction of Driver Only Operated trains.
The next 48-hour walkout takes place next week, with further strikes planned in the run-up to Christmas and over the new year.
Mr Cash said it was "despicable" that Southern "felt it necessary to try and hoodwink staff" into signing an agreement with the "sole purpose to stop lawful industrial action".
In a statement, Southern said: "Passengers have had to endure 17 days of strikes so far with 11 more to come, causing misery and hardship to people's work and family lives.
"We feel we cannot make these payments to conductors who are planning to take industrial action.
"They will be paid once the industrial action is over."
Southern rail has been accused of bullying after it asked staff to sign a pledge not to strike in exchange for getting backdated holiday pay early.