Robert Muir may refer to:

• Robert Muir (pathologist) (1864–1959), Scottish pathologist
• Robert Muir (politician) (1919–2011), Canadian politician
• Robbie Muir (footballer) (born 1953), Australian rules footballer
• Bob Muir (coach), American swimming coach in the International Swimming Hall of Fame
• Bob Muir (footballer) (1907–1973), Australian rules footballer
• Bob Muir (racing driver), Australian Bathurst 1000 race car driver
• Bobby Muir (1876–1953), Scottish footballer
• Robert Andrew Muir (1821–1904), Australian merchant and politician
• Robert Muir of Loanfoot (1758–1788), Scottish estate owner