Her sons, Toby Stephens and Chris Larkin, released a statement ... saying Smith passed away in the hospital peacefully early Friday morning. They did not give a cause of death.

Smith's family thanked the staff at the Chelsea and Westminster Hospital for their care and support during their mother's final days ... and asked for privacy during this trying time.

Maggie got her start in professional acting in the early 1950s ... kicking off her career with myriad stage appearances at some of the largest venues in England.

She transitioned to film acting ... receiving tons of praise for her role as Desdemona on the stage and onscreen alongside Laurence Olivier in "Othello." She received her first Academy Award nomination for it -- though she wouldn't win her first Oscar until "The Prime of Miss Jean Brodie" four years later.

In total, MS received six Oscar nods during her lifetime ... winning one other in 1978 for her role in "California Suite."

Younger fans will recognize her more for her 2000s roles ... appearing in seven of the eight 'Harry Potter' films as Potter's teacher, Professor Minerva McGonagall.

She then moved onto her dramatic role as Violet Crawley -- matriarch of the main family in "Downton Abbey" -- delighting fans in the snooty period piece for all six seasons and two movies. For that, she won three Primetime Emmys, three SAG Awards and a Golden Globe.

Smith dealt with her own health issues over the years, announcing she had cancer way back in 2007. However, by 2009, she'd made a full recovery and was cancer-free.

Maggie's survived by her two sons and five grandchildren.

She was 89.