The cost of producing electricity from solar energy has in the last two years been lower than that of fossil fuels — and that "permanent change" will limit how high oil prices can climb, according to Citi.

That shift is coming at a time when global oil supply is running ahead of demand, which is already weighing down on energy prices, David Bailin, chief investment officer at Citi Private Bank, said on Thursday.

As evidence of the limited upside in oil prices, Bailin pointed to last year's drones attack on the world's largest oil processing facility in Saudi Arabia. The attack on two Saudi Aramco facilities — claimed by Iran-aligned Yemen's Houthi rebels — cut Saudi oil production by half and the world's daily output by 5%.

"We saw an 11-day impact in the markets: The initial spike of as much as 8% in oil prices, and then it was 4% and then ultimately down to zero," Bailin told CNBC's "Squawk Box Asia."

"It's going to take something much bigger to make a permanent impact on oil prices and have them sustainably higher than that," he added.

A shift from oil, natural gas and coal to solar power in electricity generation will be "the ultimate cap" on prices of fossil fuels, said the CIO.

"We believe that's a permanent change. In fact, our clients were investing in that as an unstoppable trend because now you can identify that cost point, it's a great opportunity," he said.

A report released last year by the International Renewable Energy Agency predicted that electricity generated by onshore wind and solar will be consistently cheaper than any fossil fuel source starting 2020, reported Reuters. The agency is an inter-governmental body that aims to help countries transition to sustainable energy sources.