The U.S. dollar has been on a tear that threatens to derail the oil price rally and OPEC's effort to balance an oversupplied crude market, the editor of The Schork Report warned on Wednesday.

Dollar strength is being driven by forecasts for stronger economic growth and inflation in the United States than in other developed nations.

Oil prices have so far risen along with the dollar following an agreement among producing nations to cut output. But a stronger greenback typically weighs on crude futures because the commodity is priced in the currency. When the dollar rises, crude becomes more expensive to holders of other currencies.

"If we do see continued strength in the dollar that will have a double whammy on oil prices," Stephen Schork told CNBC's "Squawk Box."

First and foremost, prolonged dollar strength will inevitably crimp demand for crude oil, he explained. Lower demand will make it harder for the OPEC's output cuts to reduce huge stockpiles of crude that built up around the world following a boom in oil production.