Deputy leader Anas Sarwar revealed the party plans to repeal the Offensive Behaviour at Football and Threatening Communications (Scotland) Act if it wins the next Holyrood election in 2016.
Football fans have already voiced concerns about the legislation, which gained Royal Assent in January 2012.
Earlier this month Celtic Football Club called for a review of the law, saying there was "already sufficient evidence of the Act's unhelpfulness and negative impacts" to justify it.
But Community Safety Minister Roseanna Cunningham told a Holyrood committee at the time that holding an early review would be "nonsensical".
When the Act was brought in, the Scottish Government agreed to review its operations after two full football seasons and to report back to Parliament one year later.
The legislation gave police and prosecutors powers to tackle sectarian songs and abuse at and around football matches, as well as threats posted on the internet or through the mail, creating two distinct offences that are punishable with a range of penalties up to a maximum of five years in prison and an unlimited fine.
Some fans say the changes have created problems for ordinary supporters.
Mr Sarwar told the Daily Record: "The Offensive Behaviour at Football Act is not fit for purpose.
"It has proved to be ineffective and unpopular, not least because sectarianism runs far beyond our touchlines and our terraces."
He said Labour would tackle sectarianism with "renewed focus", concentrating on "education and prevention, not politics".
Mr Sarwar, the MP for Glasgow Central, said this would ensure "the police get the support they need and the well-meaning majority of football fans are respected".