The 32-year-old Sri Lanka leg-spinner had re-signed for the county after playing 11 times in T20 last season.
Northants already have South Africa spinner Tabraiz Shamsi lined-up for the next two games as a replacement.
"We have looked for potential replacements but we're going to stick with our own," head coach David Ripley told BBC Radio Northampton.
"It reminds me of when Seekkuge got called up for Sri Lanka last season - we hunted high and low for replacements for five games and in the end we got nowhere.
"Those five games went pretty well for us with our own and then on Finals Day we hoped Seekkuge would be back, he didn't make it but we had people step up to the plate."
Shamsi has already made an impact at Northants in this season's T20 Blast, taking 2-20 against Durham and 2-24 versus Birmingham, helping them to victories in both games.
He was due to cover only the first three games with Prasanna on international duty with Sri Lanka.
Northants spinner Seekkuge Prasanna will miss the entire 2017 T20 Blast competition with a hamstring injury.