Monte-Carlo significance test procedures consist of the comparison of the observed data with random samples generated in accordance with the hypothesis being tested. ... It is preferable to use a known test of good efficiency instead of a Monte-Carlo test procedure assuming that the alternative statistical hypothesis can be completely specified. However, it is not always possible to use such a test because the necessary conditions for applying the test may not be satisfied, or the underlying distribution may be unknown or it may be difficult to decide on an appropriate test criterion.
The test is still Fisher's. The Monte Carlo simulation is simply a way to avoid the computation space and time needed for this test when the sample size is large.
Perhaps see gung's answer here: https://stats.stackexchange.com/questions/275828/applying-monte-carlo-simulation-for-fisher-test