The agency sued PTG Capital Partners, PST Capital Group, Nedko Nedev, Strategic Capital Partners Muster and Strategic Wealth Investment, according to the wire service.
The SEC lawsuit also covers alleged false tender offers for Tower Group International and Rocky Mountain Chocolate Factory.
The agency alleges that the defendants attempted to manipulate those companies through false tender offers and press releases.
PTG, PST and Strategic Capital are all based in Sofia, Bulgaria, according to the charges. Nedev, a 37-year-old trader, is also based in Sofia, the filing said. Strategic Wealth is incorporated in Nevada and "frequently trades in parallel" with Nedev's Strategic Capital account, according to the filing.
Avon's stock was halted three times during trading on May 14 after reports surfaced that the company might be acquired by a company called PTG Capital Partners for $18.75 a share. Avon stock surged on the news, at one point as much as 20 percent, and the volume increased by about 448 percent in one day, according to the court filing.
Read MoreThe Avon Hoax and what it means
Quick research showed that there may be no such firm as PTG: The U.K. Companies House does not have a registration for a company called PTG Capital Partners.
CNBC tried to contact the firm, but the number listed on the SEC filing proposing the acquisition is a mobile phone that goes straight to voicemail.
Avon later confirmed it had not received an offer from PTG and has not confirmed the firm's existence.
The regulator said Nedev had along with others taken positions in the stocks before the alleged manipulation, hoping to sell their positions at artificially inflated prices, and that the manipulation made Nedev tens of thousands of dollars.
The Rocky Mountain case stemmed from an alleged bogus tender offer on Dec. 18, 2012 from defendant PST Capital Group Ltd to buy the confectionery retailer for a 27 percent premium, causing its shares to rise 4.6 percent.
Meanwhile, the SEC said the share price of Tower Group rose 32 percent on May 13, 2014 after a fraudulent press release was issued in the name of Euroins Insurance Corp, also from Sofia, to buy that insurance holding company. Tower was later bought by Bermuda-based ACP Re Ltd.
The SEC lawsuit seeks civil penalties and to recoup illegal profits from Nedko and the other defendants.
There is a history of shady takeover bids that have moved stocks in big ways only to be called out as hoaxes soon after. Notable examples include American Airlines and Emulex.
The idea is to drive up the stock price, sell it and turn a quick profit.
—Reuters and CNBC's Fred Imbert and Reem Nasr contributed to this report.