In a statement, Dortmund said the 28-year-old had felt unwell during a training camp in Switzerland on Monday and underwent a number of medical examinations.
He has now returned to Germany where he will undergo more tests at a specialist medical facility over the coming days.
"This news today came as a shock to Sébastien Haller and everyone else," said Dortmund's sporting director Sebastian Kehl.
"The entire BVB family hopes that Sébastien makes a full recovery as soon as possible and that we can give him a hug again soon.
"We'll do everything in our power to ensure that he receives the best possible treatment."
Haller, who has yet to publicly comment, only joined Dortmund earlier this month after an impressive spell at Dutch giant Ajax.
The Ivory Coast international scored 47 goals in 66 games for his former club during an 18 month spell, 11 of which came in the Champions League.
Dortmund requested that Haller's privacy be respected and said it would provide an update when more information is available.