Exhibit 99.1

PRESS RELEASE

Monolithic Power Systems, Inc.

983 University Avenue, Building A

Los Gatos, CA 95032 USA

T: 408-357-6600, F: 408-357-6601

www.monolithicpower.com

Monolithic Power Systems, Inc. Appoints Replacement for

Departing Venture Capital Board Member

Victor Lee Brings Over 25 Years Experience to MPS Board

LOS GATOS, Calif., September 14, 2006 – Monolithic Power Systems, Inc. (MPS) (Nasdaq: MPWR), a leading fabless manufacturer of high-performance analog and mixed-signal semiconductors, today announced the appointment of Mr. Victor Lee as a Class I director and the resignation of Mr. Jim Jones from the company’s board of directors and the compensation, audit and nominating committees.

“I am proud to have been part of the great success of MPS over these past four years,” said Jim Jones. “The company has enjoyed phenomenal growth, and I look forward to their continued success.”

“We wish to thank Mr. Jones for his commitment and service to MPS,” said Michael Hsing, president and chief executive officer. “As we move into our next phase of growth as a public company, we are extremely excited to have someone of Mr. Lee’s caliber join our board of directors. His extensive background in finance and the semiconductor industry make him an ideal addition to our board.”

“I am delighted to join the board of directors of such a dynamic company,” said Mr. Lee. “MPS has impressive power management technology, and I am excited to participate in the significant opportunity that this company has going forward.”

Mr. Lee brings over 25 years of experience in the semiconductor industry to the board of MPS. He currently serves as chief financial officer and secretary of fabless semiconductor manufacturer, Leadis Technology Inc., which he led to a successful IPO in 2004. Previously Mr. Lee served as chief financial officer and secretary of SINA Corporation, an Internet portal network company. Mr. Lee has also held senior management roles at VLSI Technology, Inc., a semiconductor manufacturer, and Advanced Micro Devices, Inc. Mr. Lee holds a B.S. in Industrial Engineering and Operations Research and an M.B.A. from the University of California, Berkeley.

About Monolithic Power Systems, Inc.

Monolithic Power Systems, Inc. (MPS) develops and markets proprietary, advanced analog and mixed-signal semiconductors. The company combines advanced process technology with its highly experienced analog designers to produce high-performance power management integrated circuits (ICs) for DC to DC converters, LED drivers, Cold Cathode Fluorescent Lamp (CCFL) backlight controllers, Class D audio amplifiers, and Linear ICs. MPS products are used extensively in computing and network communications products, LCD monitors and TVs, and a

wide variety of consumer and portable electronics products. MPS partners with world-class manufacturing organizations to deliver top quality, ultra-compact, high-performance solutions through the most productive, cost-efficient channels. Founded in 1997 and headquartered in Los Gatos, California, the company has expanded its global presence with sales offices in Taiwan, China, Korea, Japan, and Europe, which operate under MPS International, Ltd.

###

Monolithic Power Systems, MPS, and the MPS logo are registered trademarks of Monolithic Power Systems, Inc. in the U.S. and trademarked in certain other countries.

Contact:

Rick Neely

Chief Financial Officer

Monolithic Power Systems, Inc.

408-357-6777