New figures show that 22,000 claimants have started work and stopped taking benefits since the cap was introduced in April 2013. A further 11,500 have reduced their claims.
In total, 73,000 households have seen their benefits capped.
That figure is expected to rise dramatically when the maximum benefit claim per household is cut from £26,000 to £23,000 in London and £20,000 in the rest of the country.
Mr Crabb said: “The original benefit cap put an end to sky-high benefit claims and provided a clear incentive to move into work.