The authors analyze the existence of almost periodic solutions of the impulsive fractional differential equation \[ D^\alpha x(t)+ Ax(t)= F(t,x(t))+ \sum^\infty_{k=-\infty} G_k(x(t))\,\delta(t-\tau_k) \] in a Banach space \(X\). Here \(D^\alpha\) denotes the fractional time-derivative, \(\alpha\in(0,1]\), \(A\) is the infinitesimal generator of an analytic \(C_0\)-semigroup, \(G_k\) are continuous impulsive operators \(D(G_k)\subset X\to X\), \(\delta\) is Dirac’s delta function. It is shown that if \(\{\tau^j_k\}\), where \(\tau^j_k= \tau_{k+j}-\tau_k\), is uniformly almost periodic, \(F\), \(G_k\) are bounded, \(F(t,x)\) is almost periodic in \(t\), uniformly in \(x\), the sequence \(\{G_k(x)\}\) is almost periodic with respect to \(k\in Z\), uniformly in \(x\), and \(F\), \(G_k\) satisfy Lipschitz conditions, then if the Lipschitz constants of \(F\), \(G_k\) are sufficiently small, there exists a unique piecewise continuous almost periodic solution.