According to NBK, the sale would generate a profit of $87m, which would reflect in the 2014 financial result.
In 2004, National Bank of Kuwait acquired a 20% stake in IBQ and then raised its shareholding to 30% in 2007.
NBK chairman Nasser Al Sayer said: "We have decided to exit this partnership as we saw limited opportunity to increase our 30% ownership in IBQ to a controlling stake.
"This sale will also strengthen our capital position to pursue our regional expansion strategy and benefit from any opportunity in Qatar or any of the other GCC markets."
The sale is subject to customary conditions including regulatory approvals.
NBK Group CEO Isam Al-Sager said: "We view this transaction as a fruitful exit from a long term investment.
"NBK has achieved excellent returns from its investment in IBQ; not only from the gain generated from the sale but also from a decade of profit contribution from IBQ as an associate of the Group."
