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A recent model of nonlocal gravity is tested by the dynamics of the Solar System. This theory of gravity goes beyond the hypothesis of locality and includes the past history of an observer into measurements. Using the supplementary advances of the perihelia provided by INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain the bounds on its parameters: α and λ 0 . In this investigation, we take the Lense–Thirring effect due to the Sun’s angular momentum and the uncertainty of the Sun’s quadrupole moment into account. These two factors were usually absent in previous works. We find that INPOP10a yields the Solar System’s bounds as α = ( − 0.6 ± 12 ) × 1 0 − 12 and λ 0 = ( 0.2 ± 2.1 ) × 10 5 kpc, while EPM2011 gives α = ( 0.3 ± 3.2 ) × 1 0 − 12 and λ 0 = ( − 0.4 ± 1.7 ) × 10 5 kpc. The bound of α is considerably smaller than the result based on the rotation curves of spiral galaxies and the bound of λ 0 is much larger than the one based on the rotation curves by at least 5 orders of magnitude. It makes the nonlocal gravity much weaker in the scale of the Solar System than it in the scale of galaxies, implying that a screening mechanism is required to suppress the nonlocal gravity in high density regions. [ABSTRACT FROM AUTHOR]