I rented an apartment in New Jersey before starting my job, right after I had my H1-B interview and I was told my visa was approved. Now I just found out that my visa was sent for administrative processing and it might take few days to few months to get my passport back and hence be able to travel to the US. Given that I will not be able to come to my new apartment (and won't have a job until I come), is this a reason to cancel the lease without paying any early cancelation fees (I mean is there any law for this, without having to negotiate with my landlord)?
You must negotiate with the landlord. There is no guarantee that you can cancel the lease early at all, unless that is written into the lease agreement. Some landlords will tell you that having signed, it's your problem to line up another tenant to take over the lease and/or whom you could sublet the unit to (if the lease allows sublets).
If you already have the job lined up, your new employer's HR department may be able to help you resolve this. If they often hire nonresidents they have probably experienced this before, and may be in a better position to conduct the negotiations with the landlord.