The Fresh Market operates 159 stores in 22 states across the US.
Seatrade Cruise News reported his departure in August for a job outside the industry. Carnival has not announced a successor.
Before Carnival, Heaney was CFO for SeaWorld Parks & Entertainment. Earlier, he held a number of executive financial positions including CFO and SVP finance and travel operations at Disney Cruise Line, where he worked for 17 years.
Prior to that, Heaney held various financial posts at Royal Caribbean International.