The European Club Association chairman spoke out following Tuesday's announcement from a FIFA task force recommending that the tournament be held in November and December.
The proposal concludes a six-month consultation by the task force, convened to address concerns over playing the event during the Arab nation's summer months, when temperatures can exceed 40 degrees centigrade.
But the timing will have consequences for European competitions and Rummenigge wants assurances that clubs will have their losses covered.
"[The] recommendation of the task force regarding the FIFA World Cup 2022 in Qatar does not come as a surprise; it was rather expected," Rummenigge said.
"For the football family the rescheduling of the FIFA World Cup 2022 presents a difficult and challenging task. All match calendars across the world will have to accommodate such tournament in 2022/23, which requires everyone's willingness to compromise.
"However, the European clubs and leagues cannot be expected to bear the costs for such rescheduling. We expect the clubs to be compensated for the damage that a final decision would cause."
It is expected that FIFA will confirm the dates for the tournament at their next executive committee meeting in Zurich on March 19 and 20.
