Police were called to Broomlands Street at around 9.15 on Thursday morning after receiving reports of a stabbing.
A 50-year-old man has been taken to Queen Elizabeth University Hospital.
His injuries have been described as life threatening.
A 26-year-old has been arrested in connection with this incident and police are continuing their appeal for witnesses.
Police Scotland have stressed that this incident is not related to the nearby polling station or the Scottish Parliament elections, which are taking place through out the day.
Detective Inspector Ian Ross from CID said: “This has been a targeted attack, with the two individuals known to each other, and one is now in a very serious condition in hospital.
“We are appealing to anyone who witnessed the attack, has dash cam or CCTV footage, to get in touch via 101, quoting reference number 0666 of 6 May 21.”