The authors construct certain Clifford-Laguerre polynomials by taking monogenic extensions (higher dimensional Euclidean vector-valued analogues of holomorphic functions) of Laguerre polynomials. One begins with Clifford-Heaviside functions \[ P^{\pm}(x)=\frac{1}{2}\Bigl(1+i\frac{x}{| x| }\Bigr),\qquad x=\sum_{j=1}^n e_j x_j, \] where the standard basis vectors \(e_j\) satisfy the Clifford multiplication and conjugation rules \[ e_je_l+e_ke_j=-2\delta_{j,k},\qquad \overline{e_j}=-e_j. \] The Clifford-Laguerre polynomials \(L^{\pm,\pm}_{k,\alpha}(x)\) on \(\mathbb{R}^n\) arise in the so-called CK (Cauchy-Kovalevs\-kaya) extension \(\sum_{k=0}^\infty (-1)^k \frac{x_0^k}{k!} \partial_x^k f(x)\) of a real-analytic function \(f\) on \(\mathbb{R}^n\) to a {\textit{monogenic}} function in \(\mathbb{R}^{n+1}_+\), as the authors review. Here, \(\partial_x =\sum_{j=1}^n e_j \partial/\partial x_j\). For example, \(F^{\pm}(x)=\exp(-| x| )| x| ^\alpha P^{\pm}\) extends to \[ F^{+}(x)=\exp(-| x| )| x| ^{\alpha}\sum_{k=0}^\infty \frac{{x_0}^k}{k!} | x| ^{-2k}\bigl(L^{+,+}_{k,\alpha}(x)P^{+}+L^{+,-}_{k,\alpha}(x)P^{-}\bigr). \] The authors derive the orthogonality relation \[ \int \overline{L^{+,+}_{k,\alpha+2k}}\bigl(L^{+,+}_{\ell,\alpha+2\ell}P^{+} \,+\,L^{+,-}_{\ell,\alpha+2\ell}P^{-}\bigr)| x| ^\alpha \exp(-| x| ) \, dx =0 \] when \(\alpha>-n\) and \(2k<\ell\). This justifies proposing the \textit{wavelets} \[ \psi_{\ell,\alpha}(x) = \bigl(L^{+,+}_{\ell,\alpha+2\ell}P^{+}\,+\, L^{+,-}_{\ell,\alpha+2\ell}P^{-}\bigr)| x| ^\alpha \exp(-| x| ), \] which are then shown to have vanishing moments up to order \(\ell-1\). A continuous wavelet transform based on these wavelets is then discussed.