We study the Jeans mass-radius relation of Bose-Einstein condensate dark matter in Newtonian gravity. We show at a general level that it is similar to the core mass-radius relation of Bose-Einstein condensate dark matter halos [P. H. Chavanis, Phys. Rev. D 84, 043531 (2011)]. Bosons with a repulsive self-interaction generically evolve from the Thomas-Fermi regime to the noninteracting regime as the Universe expands. In the Thomas-Fermi regime, the Jeans radius remains approximately constant while the Jeans mass decreases. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. Bosons with an attractive self-interaction generically evolve from the nongravitational regime to the noninteracting regime as the Universe expands. In the nongravitational regime, the Jeans radius and the Jeans mass increase. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. The transition occurs at a maximum Jeans mass which is similar to the maximum core mass of Bose-Einstein condensate dark matter halos with an attractive self-interaction. We use the core mass-radius relation of dark matter halos and the observational evidence of a “minimum halo” (with typical radius $R\sim 1\mathrm{kpc}$ and typical mass $M\sim {10}^8{M}_{\odot }$) to constrain the mass $m$ and the scattering length $a_s$ of the dark matter particle. For noninteracting bosons, $m$ is of the order of $2.92\times {10}^{-22}\mathrm{eV}/c^2$. The mass of bosons with an attractive self-interaction can be only slightly smaller ($2.19\times {10}^{-22}\mathrm{eV}/c^2<m<2.92\times {10}^{-22}\mathrm{eV}/c^2$ and $-1.11\times {10}^{-62}\mathrm{fm}\le a_s\le 0$); otherwise, the minimum halo would be unstable. Constraints from particle physics and cosmology imply $m=2.92\times {10}^{-22}\mathrm{eV}/c^2$ and $a_s=-3.18\times {10}^{-68}\mathrm{fm}$ for ultralight axions, and it is then found that attractive self-interactions can be neglected in both the linear and the nonlinear regimes of structure formation. The mass of bosons with a repulsive self-interaction can be larger by 18 orders of magnitude ($2.92\times {10}^{-22}\mathrm{eV}/c^2<m<1.10\times {10}^{-3}\mathrm{eV}/c^2$ and $0\le a_s\le 4.41\times {10}^{-6}\mathrm{fm}$). The maximum allowed mass ($m=1.10\times {10}^{-3}\mathrm{eV}/c^2$ and $a_s=4.41\times {10}^{-6}\mathrm{fm}$) is determined by the Bullet Cluster constraint while the transition between the noninteracting limit and the Thomas-Fermi limit corresponds to $m=2.92\times {10}^{-22}\mathrm{eV}/c^2$ and $a_s=8.13\times {10}^{-62}\mathrm{fm}$. For each of these models, we calculate the Jeans length and the Jeans mass at the epoch of radiation-matter equality and at the present epoch.