We consider the problem of optimal linear estimation of the functional $$A_N \vecξ =\sum_{j = 0}^{N} (\vec{a}(j))^{\top} \vecξ(j)$$ that depends on the unknown values $\vecξ(j),j=0,1,\dots,N,$ of a vector-valued harmonizable symmetric $α$-stable random sequence $\vecξ(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$, from observations of the sequence $\vecξ(j)+\vecη(j)$ at points $j\in\mathbb Z\setminus\{0,1,\dots,N\}$. We consider the problem for mutually independent vector-valued harmonizable symmetric $α$-stable random sequences $\vecξ(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$ and $\vecη(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$ which have absolutely continuous spectral measures and the spectral densities $f(θ)$ and $g(θ)$ satisfying the minimality condition.