The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets , the formation of plasmoids , and the resultant fast magnetic reconnection . In this Letter , we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic ( MHD ) turbulence by means of high-resolution direct numerical simulations . At sufficiently large magnetic Reynolds number ( R _ { m } = 10 ^ { 6 } ) , the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets . The disruption of current sheet structures facilitates the energy cascade towards small scales , leading to the breaking and steepening of the energy spectrum . In the plasmoid-mediated regime , the energy spectrum displays a scaling that is close to the spectral index -2.2 as proposed by recent analytic theories . We also demonstrate that the scale-dependent dynamic alignment exists in 2D MHD turbulence and the corresponding slope of the alignment angle is close to 0.25 .