Two-time Grand Slam doubles champion Purcell said during the week he had "unknowingly received an IV infusion of vitamins above the allowable limit of 100ml".
The International Tennis Integrity Agency (ITIA) said that Purcell "requested to enter into a provisional suspension on December 10."
Under the ban, the 26-year-old is prohibited from playing in any tennis event, meaning he will miss the Australian Open in January where he was going to partner Thompson.
The pair won the US Open this year.
"After we won the US Open, we were like, yeah, let's go for our home Slam. Now it's not going to happen," Thompson said ahead of the Brisbane International.
"It's a stitch-up. I mean, the guy took too much salt water in an IV bag in Bali, I think. He was unwell. That's why he went there. He went to the hospital.
"I have no good words for it. It is a joke.
"I mean, guys are testing positive, performance enhancers, he's gone out and taken too much salt water, they've suspended him," he added.
Tennis Australia has stressed that the breach related to a prohibited method, rather than a prohibited substance.
"I was shattered for him. We wanted to win the Australian Open," said Thompson.
"Our last two Grand Slams was a final with match points, then go back to the next Grand Slam and we win it.
"Our goal was to get to the Australian Open and to win it. We would have been a high seed. I guess anti-doping has other ideas."
Purcell also won the 2022 Wimbledon doubles title, alongside another Australian, Matt Ebden.
