Why do you care? The computations will be almost inifinitessimal, even for a huge matrix. (Do you understand the notation O(n)?) There are only n operations to be performed here, so O(n). The only cost as the matrix gets large will be allocating and storing the array, almost all of which will be zeros.
A = rand(10000);
timeit(@() diag(1./diag(A)))
More important may be what are you doing with that matrix! The result will be a diagonal matrix. And almost the only reason you are doing that is to multiply it with another matrix. And there are better ways to do that operation! The point is, a matrix multiply scales the rows (or columns as you do it) of the final array. But a matrix multiply is the expensive part. For example...
A = rand(5000);
B = rand(5000);
Adiag = 1./diag(A);
d = diag(1./diag(A));
timeit(@() B*d)
timeit(@() B.*Adiag.')
Why are the two results that much different? THINK ABOUT IT! What is the time cost for a matrix multiply of two nxn matrices? If you don't know, then you really need to do some reading. Hint: O(n^3)
But all you want to do is perform n^2 multiplies. What is the time cost of the second form I show? HInt: O(n^2)
My point is, if you are asking this question, it is most likely you are asking the wrong question. Just because you CAN scale the rows or coluns of matrix by a constant does not mean that a good way to accomplish the task by using a matrix multiply with a diagonal matrix. And just because you see it written in a formula does not mean you should always write code that looks just like your equation. At least, that is if you care about speed.
