The answer is "no" because in general there does not even exist a neighbourhood $U$ of your submanifold that holomorphically retracts to the submanifold. In fact Finnur Lárusson has [proved][1] the following (warning: I have kept his notations, so as to faithfully quote him. In particular $[X]$ is $\mathcal O(X)$, the line bundle on $M$ associated to the divisor $X$)

> **Theorem.** Let $X$ be a connected hypersurface in a compact complex manifold $M$ of dimension at least $2$. If
> 1) $H^0 (M, TM) = 0$
> 2) $\dim H^0(M, [X]) \geq 2$, and
> 3) $H^1(M, [X]^{\vee} \otimes TM) = 0$,
>
> then no neighbourhood of $X$ retracts holomorphically onto $X$.

Note that the hypotheses are very easy to satisfy: (1) holds for $K3$ surfaces for example  and (2), (3) will follow from $X$ being sufficiently ample.


[Here][2] is a freely downloadable version of Lárusson's   article, from his homepage.

[1]:https://doi.org/10.1007/s002080050057 "Holomorphic neighbourhood retractions of ample hypersurfaces. Math. Ann. 307, No. 4, 695-703 (1997). zbMATH review at https://zbmath.org/0869.32005"    
[2]:http://www.maths.adelaide.edu.au/finnur.larusson/papers/retr.pdf