CBSE 10th

No, you cannot do master of business administration (MBA) directly after diploma. Diploma is equivalent to +2 and MBA is post-graduation course. For admission in MBA course, you'll need to be a Graduate at least, as this is a Masters or Post-Graduation Program.
With a Diploma in Engineering you 1st need to complete your graduation. If your interest lies in engineering you may go ahead with engineering course many colleges admits Diploma holders directly into the 2nd Year of the Engineering course through lateral entry examination conducted by various engineering colleges.
If you don't want to pursue Engineering any further you may take up BBA course which gives you a hint of all the factors related to Business Administration post which you can decide which stream you want to do your MBA in (MBA is offered with specialization in fields like - Marketing, Finance, Supply Chain, Operations, IT, Environment, Health and Safety, HR etc.).At the same time you can prepare for CAT, MAT and XAT to get college of your choice.
All the best.