Qatar beat bids from Australia, Japan, South Korea and the United States to win the right to host football's showpiece tournament despite temperatures in the Gulf nation reaching 50 degrees Celsius in the middle of the year.
After heavy criticism of the decision, calls were made to move it from its normal position in June and July to the end of the year when temperatures in Qatar are lower.
Football Federation Australia (FFA) chairman Lowy, the billionaire owner of the Westfield shopping centre empire, said a quick decision over the move at FIFA's executive board meeting next month risked "making a bad situation worse".
As well as the other bidders, Lowy said countries with professional leagues, like Australia's top flight A-league, which would be disrupted by the move should also be compensated.
"Our season takes place during the Australian summer to avoid a clash with other local football codes," he said.
"If the World Cup were to be staged in the middle of our A-League season it would impact on our competition, not just for 2022, but for the seasons leading up to and beyond that date.
"Clubs, investors, broadcasters, players and fans would all be affected."
FIFA president Sepp Blatter last week stood by the decision to award the tournament to Qatar, saying the decision to play the tournament in the middle of the year was the only mistake.
"FIFA has an opportunity now to make the best of a bad situation by embarking on a transparent and orderly approach, unlike the process that led to the original flawed decision in December 2010," Lowy said in a statement.
"FIFA champions the notion of 'Fair Play' and that principle should apply to the decisions it makes in the coming months."
Australia invested A$43 million (£25.18 million) in their failed bid to host the World Cup for the first time.
Lowy said the FFA had already contacted Blatter to explain Australia's position.
"Australia invested heavily in the World Cup process and the entire nation was behind the bid," he said.
"Since December 2010 Australia has been careful not to let its misgivings about the process be interpreted as sour grapes.
"But now, with increasing speculation about a change that will impact on us as one of the bidding nations, and because our competition will be affected, we have made our position public."
Lowy also suggested that no decision on the switch be made until an investigation into the 2022 bidding process by FIFA's ethics committee was completed.
"Better to let the independent investigative process run its natural course and then, with those issues settled, make a clear-eyed assessment about rescheduling and its consequences," he added.
In another blow to FIFA's hopes of switching the tournament, Fox Sports, who agreed to pay a record fee for US broadcast rights to the stage the World Cup, apparently oppose plans to move the 2022 event.
James Murdoch, the son of 21st Century Fox chairman Rupert Murdoch, are against moving the competition from June to the winter because it would clash with their coverage of the NFL in the US.
Fox paid $425m for the two-tournament, 2018-22 package in 2011 - four times what ESPN paid for the 2010 World Cup in South Africa and the 2014 finals in Brazil.
“FIFA has informed us that they are considering and voting on moving the 2022 World Cup,” Fox told Bloomberg. “Fox Sports bought the World Cup rights with the understanding they would be in the summer as they have been since the 1930s.”