Matthew, 46, carded a four-under 68 that included six birdies and two bogeys at Rancho Mirage in California.
Ai Miyazato of Japan and Spain's Azahara Munoz share the lead on five under, one ahead of the Solheim Cup star, Shiho Oyama and Lee-Anne Pace.
England's Charley Hull is three behind, alongside Michelle Wie and Lydia Ko.
Hull finished with back-to-back birdies to card a round of 70, the same score as world number one Ko and American superstar Wie.
New Zealand teenager Ko, 18, is bidding for her second straight major title after victory in the Evian Championship last year.
Scotland's Catriona Matthew is one shot off the lead after the opening round of the ANA Inspiration, the first women's major of the year.