Workmen appeared without warning last week and dismantled the monument, erected by Chechen independence leader Dzhokbar Dudayev who fought Russia's armies in the 1990s.
"I'm outraged. To move such a monument you should ask the people," Zaur Timerbayev, who lives in the city, said.
"There should be a referendum. This is a catastrophe."
Thousands of Chechens died when Soviet leader Josef Stalin deported almost the entire 500,000 population in 1944 during World War Two.
Just a 20 minute walk from the centre of Grozny, the monument -- a stone fist clutching a sword and surrounded by Chechen tombstones -- dominated a busy road junction.
After two independence wars since 1994 between Russian soldiers and Chechen forces, Kremlin-backed Ramzan Kadyrov rules.
He wants to build a new monument commemorating the Soviet deportation of the Chechens on the outskirts of the city.
"The original place for the memorial was not very convenient," Kadyrov said in comments distributed by his press service.
"The new location will include a place for ceremonies, a mosque and a composite history of the subject. An obelisk will be built with all the names of the people who died in the relocation of the Chechens."
But many Chechens were angry the memorial has been dismantled.
"I consider the removal of this monument as abuse," 59-year-old Idris Gaitukayev said.
"I was born during the time of the expulsions, many of my compatriots died and I am seriously affected by what happened during this terrible period of my people's history."
"It's difficult for me now to talk, to express my opinion about it," says Shaaman Akbulatov, from the Memorial human rights group in Grozny "This place is in the city center, it's close to the mosque, visitors drive past it. It didn't cause inconvenience to anyone. Why does it have to be moved to the city's outskirts? Who will see it now? By moving the memorial out of sight, I think they want to erase it from people's memory."
Others believe Chechnya's Kremlin-anointed president, Ramzan Kadyrov, decided to move the memorial out of consideration for visiting Russian officials, who must drive past the tombstones on their way from Grozny's airport.
Dudayev, a former Soviet air force general, emerged as head of the Chechen independence movement after the 1991 break up of the Soviet Union.
He ordered the monument to be built and it has long been associated with him and Chechen independence. A laser-guided missile killed Dudayev in 1996 at the end of the first war in Chechnya when Chechen fighters forced Russian soldiers to leave.
Güncelleme Tarihi: 03 Haziran 2008, 16:04