MSP430F5438A: GPIO Interrupt flag set

Are you describing something that happens (a) during this sequence or (b) some time later? 

If it's (a), keep in mind that setting P1IES can cause P1IFG to be set, depending on the state of the input [Ref User Guide (SLAU208Q) Sec 12.2.7.2 ("NOTE")].

If it's (b), consider that P1OUT is "undefined" at reset [Ref UG Table 12-2], so your sequence may be creating a pull-up or pull-down. You should probably set P1OUT.2 to a known value.

Whenever the pin goes from low to high that time interrupt happens but in my case it should not happen, only when it goes from high to low. Kindly suggest the configurations and problem in my case.
Note: Only restart time will happen.

Start by adding "P1OUT |= BIT2;" at the beginning of the code above. This will assure you're setting a pull-up.

If that doesn't change anything, please describe your circuit and your test sequence.

As you said "P1OUT |= BIT2; add this line but  still has the interrupt flag set high.
Any other things that can be configured?

I don't see anything obviously wrong with your configuration, so I'm guessing there's something going on outside this code fragment. That's why I asked about your circuit and your test sequence.

If (e.g.) you're using a physical button/switch to generate the edge, it's almost certain that you're seeing switch bounce, which includes both rising and falling edges.

"if (e.g.) you're using a physical button/switch to generate the edge,"

Or especially if you are just sticking a wire onto the pin of a launchpad!

It depends on if GIE is set or not but clearing P1IFG after setting P1IE is not good. If GIE is set then setting P1IE could result in an immediate interrupt. Before you try to clear P1IFG.

Setting P1IE should come last.