Indeed as said above we do get the Seiberg-Witten curve from M-theory. To do this we need to consider the following brane setup in type IIA strings:

Consider $x_0, \ldots, x_{10}$ and put $M$ $NS5$-branes in $x_0, \ldots, x_5$ and $N$ $D4$-branes in $x_0, x_1, x_2, x_3, x_6 $ (and $x_{10}$ in the M-theory setup this updates to an $M5$-brane) where the $N$ $D4$-branes are suspended between the $M$ $NS$5- branes. Then introduce $2N$ flavor branes attached to those $NS5$-branes sitting in the outermost of the configuration and extended to infinity.The resulting theory is a $d=4$ $\mathcal{N}=2$ $SU(N)^{M-1}$ gauge theory (which asymptotically is conformal). $U(1)_R$ symmetry is realized by a rotation between the $x_4$ and $x_5$ while the $SU(2)_R$ one is realized by the rotation of the $x_7,x_8$ and $x_9$. The configuration I described above is a string/gauge theory interpretation. Now if we take the tension of the branes into account, the configuration has to be modified to include the quantum effects. We can uplift this configuration to M-theory (introducing a circle $x_{10}$) and minimizing the world volume of the corresponding $M5$-brane (ex-$D4$) under fixed boundary condition will yield the Seiberg-Witten curve. This curve describes a dimension two subsurface inside the space spanned by the coordinates $x_{4},x_5, x_6,x_{10}$. Now, one is not limited to a $d=4$ theory.

It is possible to compactify in the $x_5$ to obtain a $\mathcal{N}=1$ $d=5$ theory. Once we do the compactification we T-dualize along $x_5$ to obtain a system involving $NS$5-branes and $D5$-branes in Type IIB theory. I will stop here but I think this is the reference [hep-th/9706087] to check alongside (alongside Witten's one for $d=4$ theories).