Haller, who spent two years at West Ham, joined the German giants in a £28million deal from Ajax less than two weeks ago.
He has been in Switzerland preparing for the new season, but the club released a statement explaining he has left the camp.
"Borussia Dortmund striker Sebastien Haller had to leave the BVB training camp in Bad Ragaz, Switzerland, early due to illness and has already travelled back to Dortmund.
"The 28-year-old international from the Ivory Coast complained of being unwell after training on Monday morning.
"In the course of intensive medical examinations, a tumour was finally discovered in the testicles during the course of the day.
"During the coming days, further examinations will take place in a specialised medical centre."
BVB sporting director Sebastian Kehl said: "This news today came as a shock to Sebastien Haller and to all of us.
"The entire BVB family wishes Sebastien a full recovery as soon as possible and that we can hug him again soon.
"We will do everything in our power to ensure that he receives the best possible treatment."
The statement continued: "Borussia Dortmund asks that the privacy of the player and his family be respected and that no questions be asked.
"As soon as we have further information, we will inform you in consultation with the player."
Rice, who played with Haller in the Premier League, tweeted: "Thoughts are with you my brother. Praying you have a speedy recovery."
West Ham, meanwhile, added: "We're with you, @HallerSeb. Wishing you the best with your recovery."
talkSPORT's Trevor Sinclair tweeted: "Wishing you healthy recovery young man."