Is there any statistical tool available to test the hypothesis regarding differences in means of two independent non-randomly selected samples. Is Mann-Whitney-Wilcoxon test suitable for such conditions?
If you can specify what non-randomness implies exactly, there are likely to be (many) ways of modelling it. Whole fields of statistics can be thought of as different answers to that broad question (e.g. time series analysis, survey statistics).
If you are asking for a test that somehow automatically corrects for non-randomness, it can't exist. Suppose I say to you:
Sample 1 is 1,2,3 and sample 2 is 4,5,6. The two samples may differ for two reasons (1) non-random sampling (2) the populations may differ. Now correct for (1) and then tell me if (2) is true.
Without more information, the problem is insoluble. Real problems can be larger and more complicated, but the same difficulty bites.
Detail: Mann-Whitney-Wilcoxon is a not a test for means differing (except with extra assumptions that are usually gratuitous).