Repunit

First factorize $693=9 \times 7 \times 11$

Let $N$ be such repunit number.So, $N$ is divisible by 9.The number of digits should be $9 k$ where $k \in N$ .Also $N$ is divisible by $11$ . So, the sum of odd positioned digits will be same as even positioned digits.Therefore, number of digits should even.Then number of digits will be like $18 k$ .

$N$ is also divisible by $7$ .

$111 \equiv -1 \pmod{7}$ and $1000 \equiv -1 \pmod{7}$ .Then $111 \times 1000=111000 \equiv 1 \pmod{7}$

$111000+111=111111 \equiv 0 \pmod{7}$ .Here number of digits are $6$ .As $18$ is divisible by 6.

So, smallest number has $\boxed{18}$ digits which is divisible by $693$