The departure, effective March 3, comes with Turquoise Hill and global miner Rio locked in a protracted dispute over funding for the underground expansion of Rio's massive Oyu Tolgoi copper-gold mine in Mongolia.
The Anglo-Australian miner also faces renegotiation of an expansion agreement with Mongolia, which owns a 34% stake in the mine. Rio owns 51% of Turquoise Hill, which in turn owns 66% of the mine.
Turquoise Hill said on Thursday a board committee told Quellmann that Rio believed new leadership was "necessary" to advance the mine expansion.
Rio also advised it would vote against Quellmann's re-election at the annual shareholders' meeting in May, Turquoise Hill said.
Mongolia is seeking added benefits including more tax revenue from the mine after costs for the expansion ballooned to $6.75 billion, about $1.4 billion higher than Rio's estimate in 2016.
A government source said on Thursday that Ulaanbaatar is disappointed with Quellmann's sudden exit because it disrupts the continuity of negotiations.
"In our view he was doing what he was supposed to do," the source said.
Turquoise Hill said its former finance chief, Steeve Thibeault, will replace Quellmann on an interim basis.
Thibeault led negotiations for funding agreements with Rio in 2015 but has had no affiliation with either company since April, 2017, it added.
Bank of Nova Scotia analyst Orest Wowkodaw said Quellmann's departure "significantly reduces" the likelihood of a non-dilutive gold streaming transaction to help fund the mine expansion.
Rio said it remains committed to working with both Turquoise Hill and the government.
"Aligning and coordinating our joint efforts to resolve the concerns of the Government of Mongolia going forward is of the highest priority," the company said.
Toronto-listed shares of Turquoise Hill fell as much as 8.5% in mid-afternoon trading.
(Reporting by Arundhati Sarkar in Bengaluru; additional reporting by Jeff Lewis in Toronto; Editing by Devika Syamnath and Chris Reese)
By Arundhati Sarkar and Jeff Lewis