The decision to crack down on the posts comes after this summer's World Cup in Brazil, which saw thousands of football fans share footage of goals using Vine.
However, fans have been warned that posting clips is illegal and a breach of copyright.
Dan Johnson, director of communications at the Premier League, told BBC Newsbeat: "You can understand that fans see something, they can capture it, they can share it, but ultimately it is against the law.
"It's a breach of copyright and we would discourage fans from doing it. We're developing technologies like gif crawlers, Vine crawlers, working with Twitter to look to curtail this kind of activity.
"I know it sounds as if we're killjoys but we have to protect our intellectual property."
Twitter responded with the following statement: "Vine