John Kane, a full-time carer for his disabled partner, won the seat in the City Chambers with a substantial majority. He defeated SNP candidate Helen Walker.
The by-election was held following the recent death of former SNP group leader Allison Hunter.
Labour's win means Govan is the only seat on the council which has no representative from the Nationalists.
And the party's deputy leader Anas Sarwar, whose constituency takes in Govan, said: "Govan has elected a great new councillor in John Kane and I am delighted the hard work he has put over the last few weeks with the Labour team has achieved this stunning result.
"I am proud so many people turned out to support Labour and delivered us our first ever by-election win in Govan."
Govan also forms part of the Holyrood constituencies of Deputy First Minister Nicola Sturgeon and Scottish Labour Party leader Johann Lamont.
The SNP had hoped to win control of the City Chambers at the council elections in May last year.
Instead, Labour obtained an overall majority and Mr Kane's win in Govan further strengthens the party's position. Labour now has 45 councillors, the SNP 26, the Liberal/Democrats, Tories and Glasgow First one each and the Greens five.
Mr Sarwar said: "This is a devastating result for Nicola Sturgeon - this isn't just her back yard, it's her front room.
"By ensuring the SNP has no representation in Govan in the council, the people of this area have sent Nicola Sturgeon and the nationalists a strong message - stop obsessing about separation and start putting the interests of the people of Scotland first."
Council leader Gordon Matheson said support for the Nats in Glasgow has slumped. He added: "There's no way the SNP can spin their way out of this dramatic result. What odds would the bookies have given a year ago on Govan ward being SNP free?"
Graeme Hendry, SNP group leader on the council, congratulated Mr Kane on his win.
But he added: "I hope he will fight for the people of Govan rather than slavishly follow the party line. Helen deserves huge credit for putting in such a great effort and has done both herself, her party and Allison Hunter's legacy proud.
"While we wish Councillor Kane well, it was disappointing to see the Better Together campaign intervened in a Council by-election by delivering an eve-of-poll letter to Govan voters. This development is concerning for the good running of our democratic processes and should be discouraged."