We analyze the data from two recent experiments designed to search for solar axions within the context of multidimensional theories of the Kaluza-Klein type. In these experiments, axions were supposed to be emitted from the solar core, in $M1$ transitions between the first excited state and the ground state of ${}^{57}\mathrm{Fe}$ and ${}^{7}\mathrm{Li}.$ Because of the high multiplicity of axionic Kaluza-Klein states which couple with the strength of ordinary QCD axions, we obtain much more stringent experimental limits on the four-dimensional Peccei-Quinn breaking scale ${f}_{\mathrm{PQ}},$ compared with the solar QCD axion limit. Specifically, for the ${}^{57}\mathrm{Fe}$ experiment, ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}1\ifmmode\times\else\texttimes\fi{}{10}^{6} \mathrm{GeV}$ in theories with two extra dimensions and a higher-dimensional gravitational scale ${M}_{H}$ of order 100 TeV, and ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}1\ifmmode\times\else\texttimes\fi{}{10}^{6} \mathrm{GeV}$ in theories with three extra dimensions and ${M}_{H}$ of order 1 TeV (to be compared with the QCD axion limit, ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}8\ifmmode\times\else\texttimes\fi{}{10}^{3} \mathrm{GeV}).$ For the ${}^{7}\mathrm{Li}$ experiment, ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{5} \mathrm{GeV}$ and $3.4\ifmmode\times\else\texttimes\fi{}{10}^{5} \mathrm{GeV},$ respectively (to be compared with the QCD axion limit, ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}1.9\ifmmode\times\else\texttimes\fi{}{10}^{2} \mathrm{GeV}).$ It is an interesting feature of our results that, in most cases, the obtained limit on ${f}_{\mathrm{PQ}}$ cannot be coupled with the mass of the axion, which is essentially set by the (common) radius of the extra dimensions.