The 30-year-old, who is in his second stint at Scotstoun, has made 19 appearances for Glasgow, most recently as a replacement in the 40-12 win over Zebre earlier this month.
Kennedy, Price and Dobie are in the 32-man Glasgow squad which has travelled to South Africa this week for the United Rugby Championship double-header against DHL Stormers, on Friday, and Vodacom Bulls, seven days later.
“I'm happy to be staying with the club,” Kennedy told glasgowwarriors.org.
“There's a strong group of scrum-halves at the club and it's great to compete against them every week for the jersey. Despite being a more senior player, I learn new things every day and I have a great time doing it.
"The club feels like we're building towards something and I’m looking forward to continuing to be a part of it.”
Glasgow Warriors did not reveal the length of the new contract but said the player was “pledging his immediate future to the Scotstoun outfit ahead of the 2022/23 campaign”.
Kennedy rejoined Glasgow in August 2019, initially on a one-year partnership contract with Stirling County. He had previously been on loan at the club in the 2012-13 season.
The Scotland sevens international also made 66 appearances over an eight-year stint at Edinburgh and had a loan spell at London Irish in 2014.