The billboard, on the A61 at Kelham Island, appears to have been daubed with pink paint - showing Clarke's head painted over with that of a pig.
Both Blades and Owls fans refer to each other as pigs - and Clarke, who was sent off in Saturday's South Yorkshire derby against Barnsley has played for both sides.
The picture of the billboard was shared on Twitter by user "KikoOBrien8," who wrote: "What's happening? Not much twitter just a day in the life of the steel city #thecityisours #ftb #wawaw."
The picture, which has already been shared dozens of times, is to advertise Sky Sports Football, a new channel dedicated to soccer and advertising firm JCDecaux, which owns the billboard, has placed hundreds of the posters around the country, with the posters featuring local stars.
There are some suggestions that the picture may have been photoshopped.
Clarke, who joined the Blades in 2016, is one of several players to cross the Steel City divide, having played for Wednesday between 2007 and 2010.
The striker joined the Owls from Wolves and netted 18 goals in 83 appearances for the club before moving to QPR.
He signed a three-year deal with the Blades last summer after joining from Bury and has scored seven goals in 24 appearances for the Blades.
He was shown the red card along with Barnsley skipper Angus McDonald after the pair clashed in an off the ball incident during Saturday's 1-0 win for the Blades.
Fans of each club refer to the other as pigs - Wednesday's Hillsborough stadium was built on a pig farm according to legend, while Owls fans have commented that Blades' red and white striped shirts resemble streaky bacon.
It is not the first time a city centre billboard has sparked upset and controversy for Sheffield United fans.
In 2015, a controversial billboard featuring Carlos Tevez was removed from outside Bramall Lane after an outcry from supporters.
The massive billboard of Tevez celebrating scoring against Manchester United on the day his West Ham team helped relegate Sheffield United was placed just yards from the ground.
The controversy around the poster centred around what became known as the Tevez affair, a bitter row between Sheffield United and West Ham about the circumstances of the Blades’ relegation from the Premier League in 2007.
Back in 2007 Tevez, and teammate Javier Mascherano was part owned by West Ham and businessman Kia Joorabchian’s Media Sports Investment (MSI) company, an arrangement which breached Premier League rules.
Just weeks before the end of the season the Premier League decided against punishing West Ham with an expected points deduction, and instead fined them Â£5.5 million, and allowed the Argentinian pair to appear for the club for the rest of the season.
On the final day of the season Tevez scored the winner for the East London club against Manchester United at Old Trafford, a goal which ensured his team’s Premier League safety and help condemn the Blades to relegation to the Championship.
Had West Ham been docked points for fielding Tevez and Mascherano, they would have been relegated and Sheffield United would have been safe.
The affair sent shockwaves through the world of football and legal wrangling between the two clubs lasted until 2009 when an out of court settlement was agreed which saw West Ham pay the Blades Â£20 million in compensation for the relegation.