Anderson suffered the injury while bowling for Lancashire on the first day of their County Championship meeting with Somerset at Old Trafford this week.
The 40-year-old was forced off the field and played no further part across the final three days of the game, which ended in a draw on Sunday afternoon.
Anderson underwent a scan on Saturday night, with England now confirming a “mild strain” to the seamer’s right groin.
England are expected to announce a squad for the one-off four-day Test against Ireland at Lord’s, which starts on June 1, over the coming days. Anderson will be assessed in the build-up but the news that the injury does not appear to be more significant will come as a major relief with a view to this summer’s Ashes series, with the First Test against Australia at Edgbaston still a month away.
England are already set to be without fast bowler Olly Stone due to a hamstring injury, while there remains uncertainty about Jofra Archer’s hopes of playing any part in the series after the 28-year-old returned home early from the Indian Premier League this week in order to rest a nagging elbow injury.