For a moment let's assume you subscribe to the Hamiltonian used by Fu-Kane to describe the TI surface with an induced superconducting proximity effect,
\begin{equation}
\mathcal{H}(\mathbf{k})=\left(
\begin{array}{cc}
H(\mathbf{k}) & i\sigma_y \Delta \\
-i\sigma_y \Delta^* & - H^*(-\mathbf{k})
\end{array}
\right)=v_F(\sigma_x k_y-\tau_z\sigma_y k_x) - \tau_z\mu +\tau_y\sigma_y\Delta,
\end{equation}
where $H(k)=v_F(\sigma_x k_y-\sigma_y k_x)$ and $\Delta=\Delta(\bf{x})$ some spatially dependent single valued function. The energy eigenvalues for constant $\Delta(x)=\Delta_0$,
\begin{equation}
E=\pm\sqrt{|\Delta|^2 +(v_F |\bf{k}|\pm \mu)^2}.
\end{equation}
Let's assume for a moment that $\mu=0$, for without this condition you get flat-band Majoranas (ArXiv: http://arxiv.org/abs/1207.5534 PRB: http://link.aps.org/doi/10.1103/PhysRevB.86.161108 shameless self-publicity).
The energy eigenvalues will be written as
\begin{equation}
E=\pm\sqrt{|\Delta|^2 +(v_F \,k)^2}.
\end{equation}
This energy dispersion does not pass through $E=0$ and is not linear, $E\propto k$, but if we did set $\Delta=0$ the energy dispersion does fall into the form of a linear Dirac-like spectrum, $E=\pm v_F\,k$. But, how can we set $\Delta=0$ in a superconductor? The answer first provided by Jackiw-Rebbi (http://link.aps.org/doi/10.1103/PhysRevLett.37.172) and then by Read-Green (http://link.aps.org/doi/10.1103/PhysRevB.61.10267).
The "mass term", in this case $\Delta$ must go through a transition spatially from $+|\Delta(\bf{x})|\rightarrow-|\Delta(\bf{x})|$, which forces $\Delta(\bf{x})=0$ at exactly one point. One way to do this is by having the superconductor be in a vortex where $\Delta(r,\phi)=\Delta(r) e^{i\phi}$. Right at the center of the vortex, $\Delta(r,\phi)$ must go to 0, because there can be no value satisfies the vortex. One one point on the side of the vortex $\Delta(r_0,\phi_0)=|\Delta|$ while the opposite side, $\Delta(-r_0,\phi_0)=\Delta(r_0,\phi_0+\pi)=-|\Delta|$ because of the $e^{i\pi}$ phase difference between the two locations. This allows one location to host the Majorana fermion where the energy dispersion is linear. There are other requirements for the Majorana, but this is what I can offer at the moment. Once my thesis is in complete form (~ two weeks as of this writing), I'll post a link here because I attempt to explain your question in its introduction.
Another perspective to understanding this story is through a simpler model, a Josephson \pi junction. See the first PRB paper referenced above for my attempt at explaining this Majorana through Andreev bound states.
If you have any additional questions, please comment away. Thanks.
Update: Thesis can be found here http://lababidi.me/dissertation.pdf
