Background: The Fe51(p,γ)Co52 reaction lies along the main rp-process path leading up to the Ni56 waiting point. The uncertainty in the reaction Q value, which determines the equilibrium between the forward proton-capture and reverse photodisintegration Co52(γ,p)Fe51 reaction, contributes to considerable uncertainty in the reaction rate in the temperature range of interest for Type I x-ray bursts and thus to an ≈10% uncertainty in burst ashes lighter than A=56. Purpose: With a recent Penning trap mass measurement of Co52 reducing the uncertainty on its mass to 6.6 keV [Nesterenko, J. Phys. G 44, 065103 (2017)JPGPED0954-389910.1088/1361-6471/aa67ae], the dominant source of uncertainty in the reaction Q value is now the mass of Fe51, reported in the 2016 atomic mass evaluation to a precision of 9 keV [Wang, Chin. Phys. C 41, 030003 (2017)1674-113710.1088/1674-1137/41/3/030003]. A new, high-precision Penning trap mass measurement of Fe51 was performed to allow the determination of an improved precision Q value and thus new reaction rates. Method: Fe51 was produced using projectile fragmentation at the Coupled Cyclotron Facility at the National Superconducting Cyclotron Laboratory, and separated using the A1900 fragment separator. The resulting secondary beam was then thermalized in the beam stopping area before a mass measurement was performed using the LEBIT 9.4T Penning trap mass spectrometer. Results: The new mass excess, ME=-40189.2(1.6) keV, is sixfold more precise than the current AME value, and 1.6σ less negative. This value was used to calculate a new proton separation energy for Co52 of 1431(7) keV. New excitation levels were then calculated for Co52 using the nushellx code with the GXPF1A interaction, and a new reaction rate and burst ash composition was calculated. Conclusions: With a new measured Q value, the uncertainty on the Fe51(p,γ) reaction rate is dominated by the poorly measured Co52 level structure. Reducing this uncertainty would allow a more precise rate calculation and a better determination of the mass abundances in the burst ashes.