In general the answer is going to be that no, it will not cause any issues. Immigration officers are trained to look for features beyond those that may be covered by hair, so although they may need to look a little closer at you to determine that the photo matches, they will still be able to confirm your identity.
However there is one place where this may cause issues if you have an "e-Passport" (sometimes called a "biometric passport"), which contains a copy of your photo on the chip contained within the passport. In some countries, e-Passports allow you to use automated immigration devices, such as SmartGate in Australia or Global Entry in the US.
Depending on the size of the beard, it is very likely that the automated device will not be able to confirm that the photo on the passport matches your current image, and they will likely send you to a human to confirm the identity match. Other than being a little slower than going the automated path this won't cause any issues - it just might add a little time depending on how long you need to wait in line to see an immigration officer. Worst case, it should be no slower than not using the automated system at all.