He was taken to hospital but his condition was not clear on Saturday night.
A 21-year-old man was arrested in connection with the attack and he remains in police custody.
Bedfordshire Police said: “A man has been arrested in connection with an incident in Bedford this afternoon (Saturday), in which a man was stabbed.
“At around 4pm, we were called to a report that a man had been stabbed as he sat in his car in Maitland Street.
“The man in his 60s was taken to hospital with multiple stab wounds to his chest and neck.
“A 21-year-old man has been arrested in connection with the incident and is currently in police custody for questioning.”
Detective Chief Inspector Marie Gresswell said: "We are working to establish the circumstances of this incident, and are following up several lines of enquiry.
"We believe this was an isolated incident with no risk to the wider public, and our officers remain on scene to give reassurance to residents and listen to any concerns they may have.
"We would also like to hear from anyone who may have been in the area at that time and has any dashcam footage, CCTV, or information, which could help us in our investigation."
Anyone with information should contact police through the force’s online reporting centre, by calling 101, quoting reference number 305 of 5 June, or by calling independent charity Crimestoppers, anonymously, on 0800 555 111.