The 63-year-old Jenner received 30 stitches Monday and "will probably have a big scar on his nose," a source told the celebrity news website Thursday.
His face was partially bandaged when he was seen getting his morning coffee Tuesday in Calabasas, Calif., TMZ said.
Jenner previously had cancerous tissue removed from the side of his face last year.
Notable deaths of 2014 [PHOTOS]
Tatiana Maslany to make her New York stage debut