Microfluidic separation of magnetic particles is based on their capture by magnetized microcollectors while the suspending fluid flows past the microcollectors inside a microchannel. Separation of nanoparticles is often challenging because of strong Brownian motion. Low capture efficiency of nanoparticles limits their applications in bioanalysis. However, at some conditions, magnetic nanoparticles may undergo field-induced aggregation that amplifies the magnetic attractive force proportionally to the aggregate volume and considerably increases nanoparticle capture efficiency. In this paper, we have demonstrated the role of such aggregation on an efficient capture of magnetic nanoparticles (about 80 nm in diameter) in a microfluidic channel equipped with a nickel micropillar array. This array was magnetized by an external uniform magnetic field, of intensity as low as 6-10 kA/m, and experiments were carried out at flow rates ranging between 0.3 and 30 μL/min. Nanoparticle capture is shown to be mostly governed by the Mason number Ma, while the dipolar coupling parameter α does not exhibit a clear effect in the studied range, 1.4 < α < 4.5. The capture efficiency Λ shows a strongly decreasing Mason number behavior, Λ∝Ma^{-1.78} within the range 32 ≤ Ma ≤ 3250. We have proposed a simple theoretical model which considers destructible nanoparticle chains and gives the scaling behavior, Λ∝Ma^{-1.7}, close to the experimental findings.