I am current studying abroad and am planning to apply for a B1 visa to go to a conference in US. Will there be a problem in my B1 visa application, considering I got married to a US citizen a month before my interview?

It depends... if your husband lives in US, and you don't, you may not be able to obtain B-1/B-2, but if he lives in your country, you can submit evidences that prove he is going to stay long term there such as work contract, etc. In this case you will get B-1/B-2.