The Competition and Markets Authority (CMA) said between 2013 and 2018 Fender attempted to restrict online discounting for its guitars, as part of a provisional decision.
Piano maker Casio was fined £3.7 million in August for a similar practice, known as resale price maintenance (RPM), where retailers are forced to charge a minimum price, making competition and discounting impossible.
Fender now has an opportunity to appeal against the decision, before it is made final and any potential fine is imposed.
Ann Pope, CMA senior director of antitrust, said: "Shopping online can make it much easier to compare prices and hunt down bargains - this can be especially important for potentially big purchases like a guitar.
"We take allegations of RPM very seriously because it removes one of the benefits of the internet of making it easier to quickly find a better price by shopping around.
"It stops online retailers from selling at the prices they want to, and this then leads to higher prices for customers."
According to the CMA, guitar sales in the UK are around £440 million a year, with online sales of musical instruments now accounting for 40% of all purchases.
A Fender Europe, Middle East and Asia spokesman said: "Fender is co-operating fully with the CMA's investigation and we are reviewing the provisional findings. Due to the ongoing legal process, we will not comment further at this time."
The RPM practice is outlawed in the EU and several high-profile cases have led to fines and censures.
Last year the European Commission imposed on Philips, Asus, Denon & Marantz, and Pioneer fines totalling £99 million for artificially inflating prices.
The CMA has also fined the light fittings sector, the bathroom sector and refrigerator industry for all making similar attempts at inflating prices.