A Suzuki 2-group is defined to be a pair \((G,T)\), where \(G\) is a nilpotent 2-group of bounded exponent and \(T\) is an Abelian group that acts on \(G\) by automorphisms so that the action of \(T\) on the involutions of \(G\) is transitive. If, in addition, \(T\) acts on \(G\) freely, \((G,T)\) is called a free Suzuki 2-group. Let \(\Gamma\) denote the corresponding semidirect product of \(G\) and \(T\). The Suzuki 2-group \((G,T)\) is said to be of finite Morley rank if \(\Gamma\) with distinguished subgroups \(G\) and \(T\) is a group of finite Morley rank. Free Suzuki 2-groups of finite Morley rank appeared in the study of groups of finite Morley rank with a weakly embedded subgroup by T.~Altınel, A.~Borovik, G.~Cherlin, and E.~Jaligot, which was a part of the program of classification of infinite simple groups of finite Morley rank inspired by the Cherlin-Zilber Conjecture. In that study some results and methods of the paper under review had been used. The main result of the paper is: If \((G,T)\) is a free Suzuki 2-group of finite Morley rank with infinite \(G\) then \(G\) is Abelian. For any Suzuki 2-group \((G,T)\), if \(I\) is the subgroup of all elements of order at most 2 in \(G\) then the action of \(T/C_T(I)\) on \(I\) is known to be isomorphic to the natural action of \(K^*\) on \(K^+\), for some field \(K\); if \((G,T)\) is of finite Morley rank and \(G\) is infinite, \(K\) is known to be algebraically closed. The following results are obtained in the course of the proof for an arbitrary Suzuki 2-group \((G,T)\). If \(K\) is perfect, \(G'\leqslant I\), and \(\{g\in G:g^4=1\}\) is an Abelian subgroup then \(G\) is Abelian. If \(K\) is quadratically closed then \(G\) has a unique maximal Abelian \(\Gamma\)-normal subgroup.