Because, as noted by dbr, there can be no wash sales on realized capital gains, you do not have to wait at all for tax reporting reasons. You will have to wait until the next trading session to repurchase the same mutual fund from the same fund company/brokerage, however, because mutual fund trades are only executed once a day at the close of the session. Whether there are frequent trading limitations enforced by the fund and/or financial institution where the fund is held is another question. I suppose if you really hated to be out of the market for a day you could repurchase the fund at a different financial institution on the same day, but that does seem to be a lot of work to reset the cost basis by $200.
However, the larger question posed by retiredjg is, do you really want to keep the actively managed fund?
Poking around at M* a little bit revealed that the fund has had very favorable returns, over many different periods, compared to what I would consider the quintessential core international fund, Vanguard Total Intl Stock Index (VGTSX). However, the total international fund is far more diversified, with a market cap weighted mix of over 6000 holdings of large and small, value and growth, and developed and emerging market companies. By contrast, the Oakmark International fund has a mere 56 holdings, with no small cap exposure and no emerging markets exposure. Surprisingly, over the last 3 year period OAKIX has had a lower tax cost ratio than VGTSX. (I wonder if the recent shift to a more complete index affected the tax costs of the index fund.) Another positive attribute of OAKIX is that it's had the same fund manager for the last 20 years. (Is he due to retire soon?)
So in weighing the opportunity that your potential tax-free sale affords, I suppose one question is, would you benefit from obtaining lower cost, better diversified exposure to emerging markets in VGTSX, as opposed to obtaining your emerging markets exposure elsewhere? Also, if you are a long term buy-and-hold investor, someday you will presumably have too much in unrealized capital gains to make it worth selling OAKIX. Then if the fund management or tax attributes have changed for the worse you'll be stuck with it.