A new pyroxene compound, NaMnGe2O6, has been synthesized at 3 GPa and 800 degrees C and fully characterized by X-ray single-crystal diffraction, neutron powder diffraction, and measurements of magnetization and specific heat. NaMnGe2O6 crystallizes into a monoclinic C2/c structure with unit-cell parameters a = 9.859(2) angstrom, b = 8.7507(18) angstrom, c = 5.5724(11) angstrom, and beta = 105.64(3)degrees at 153 K.A cooperative Jahn-Teller distortion is formed by an ordering of the longest Mn-O bonds between two neighboring octahedra along the chain direction. This feature distinguishes NaMnGe2O6 from other pyroxene compounds without Jahn-Teller active cations and suggests that the Jahn-Teller distortion competes with the intrinsic local distortion in the pyroxene structure. No orbital order-disorder transition has been found up to 750 K. Like other alkali-metal pyroxenes with S > 1/2, NaMnGe2O6 (S = 2) was found to undergo a long-range antiferromagnetic (AF) ordering at T-N = 7 K due to intrachain and interchain exchange interactions. Due to the peculiar structural features and the corresponding magnetic coupling, the weak AF spin ordering gives way to a ferromagnetic-like state at a sufficiently high magnetic field. Specific-heat measurements demonstrated that a large portion of the magnetic entropy, >60%, has been removed above T-N as a result of strong spin correlations within the quasi-one-dimensional Mn3*-spin chains. The Reitveld refinement of neutron powder diffraction data gives a commensurate magnetic structure defined by k = [0 0 0.5] with Mn moments aligned mainly along the c-axis with a small component along both a- and b-axes.