It was reportedly shown during Saturday's John Smith's Stadium clash and is in reference to Marcos Alonso's involvement in a car accident in 2011 that tragically killed a young woman.
It read: "Marcos Alonso - He murdered a girl” and also contained a no drinking sign and the picture of a car.
Alonso was arrested and charged with various offences, including speeding and being over the legal alcohol limit.
After initially facing a prison sentence, Alonso was fined €61,000 and banned from driving for three years and four months.
The banner appears to have been motivated by the Spanish left wing-back's double against Spurs earlier in the season in Tottenham's opening Premier League match at Wembley.
The club now intend to identify those responsible and take action due to its "extremely poor taste."
A Tottenham Hotspur spokesman told the Times: "This banner is clearly in extremely poor taste and we are investigating the matter. If found to be a Spurs fan, they will be dealt with accordingly."