Clarke has been shortlisted for the monthly award alongside Burton Albion's Mark Duffy, Shrewsbury Town winger Sulley Kaikai and Wigan Athletic striker Will Grigg.
The winner of the award will be announced on Friday (8 April 2016) morning.
With Clarke in defence, City won four out of their six games during the month of March. The Bantams also kept three clean sheets, conceding just four goals.
As well as helping to keep it tight at the back for the Bantams, Clarke also contributed two assists for City's goals against Millwall and Crewe Alexandra.