I looked up briefly at a petroleum engineering degree curriculum, and I noticed that while there are a few fairly specialized classes, the core of the curriculum is similar to that of a mechanical engineering degree: Calculus, I, II, Chemistry I, II, Fluids, Differential Equations, etc. That being said, I think you have nothing to worry about. Now the question is what area of mechanical engineering your master studies will focus on? Is it Fluids? Is it Structural Mechanics? I noticed there are not too many classes related to Structural Mechanics (e.g. Finite Element Analysis, Strength of Materials, etc) in the petroleum engineering curriculum, but I did see Statics and Mechanics (I know different universities have different curricula, but I assume most of them should have Statics and mechanics).
So I think the answer to your question boils down to two main things:
1. What area of mechanical engineering you will be focusing on
2. How much of a hard worker are you – you may be in the position of having to catch up on few concepts (I transferred from a foreign university. The school in US agreed to transfer my credits for Thermodynamics I class, but not Thermodynamics II. So I registered to take Thermo II in USA assuming Thermo I class I took back home was similar as Thermo I offered in USA. But that wasn’t the case. So I had to catch up on Thermo I based on the USA manual while studying Thermo II – it wasn’t easy but it is do-able).
I think engineers in general are able to adapt to changes easily, and the fact that you graduated with an engineering degree and the fact that your grades are eligible to enroll in a Master program tell me that you have what it takes to succeed.