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 M 1 transitions between the first excited state and the ground state of ^ { 57 } Fe and ^ { 7 } 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 _ { PQ } , compared with the solar QCD axion limit . Specifically , for the ^ { 57 } Fe experiment , f _ { PQ } \gtrsim 1 \times 10 ^ { 6 } { GeV } in theories with two extra dimensions and a higher-dimensional gravitational scale M _ { H } of order 100 TeV , and f _ { PQ } \gtrsim 1 \times 10 ^ { 6 } { GeV } in theories with three extra dimensions and M _ { H } of order 1 TeV ( to be compared with the QCD axion limit , f _ { PQ } \gtrsim 8 \times 10 ^ { 3 } { GeV } ) . For the ^ { 7 } Li experiment , f _ { PQ } \gtrsim 1.4 \times 10 ^ { 5 } { GeV } and 3.4 \times 10 ^ { 5 } { GeV } , respectively ( to be compared with the QCD axion limit , f _ { PQ } \gtrsim 1.9 \times 10 ^ { 2 } { GeV } ) . It is an interesting feature of our results that , in most cases , the obtained limit on f _ { PQ } can not be coupled with the mass of the axion , which is essentially set by the ( common ) radius of the extra dimensions .