The TV star, who is best known for her roles in Emmerdale, Victoria and Doctor Who, stopped to take photos with fans as she walked along Argyle Street in the trendy Finnieston area of city.
Jenna, 31, is playing the lead role in the BBC One adaptation of psychological thriller, The Cry.
She was joined on set by fellow actress Sophie Kennedy Clark.
The four-part series will tell the story of a woman who travels with her husband Alistair and their baby from Scotland to Australia to see Alistair’s mother.
They try to fight for custody of Alistair’s daughter Chloe against his Australia ex-wife but are faced with a devastating tragedy that changes their lives forever.
The series, adapted from the novel by Australian author Helen Fitzgerald, has been written by Jacquelin Perske.
Elizabeth Kilgarriff, BBC Drama senior commissioning editor, and Gaynor Holmes, BBC Drama commissioning executive, said: “We’re very excited to have started filming in Australia and to have such an incredible array of Australian talent joining Jenna and Ewen, topped off with some of Scotland’s most accomplished actors.
“Watching them bring Helen FitzGerald’s gripping, page-turner novel and Jacquelin Perske’s wonderful scripts to life is a joy and we can’t wait for BBC One audiences to see The Cry.”