Strauss was heard by viewers who were watching the coverage on Fox Sports in Australia but the comments were not broadcast on British television.
He made the remarks while speaking to fellow Sky Sports commentator Nick Knight.
"I apologise unreservedly, particularly to Kevin Pietersen," Strauss was quoted as telling British media. "I am mortified and profusely sorry."
Sky Sports also said sorry for the incident earlier in the day.
"Comments were made during a break of play which were heard overseas. We apologise for the language used," the broadcaster said on its Twitter account.
The South African-born Pietersen, who was sacked by England after the 5-0 Ashes defeat in Australia earlier this year, was dropped for a test against South Africa in 2012 after sending provocative texts about Strauss to the opposition.
The match at Lord's, won by the MCC (Marylebone Cricket Club) by seven wickets, was held to celebrate the bicentenary of the historic ground.
(Reporting by Josh Reich, editing by Tony Jimenez and Toby Davis)
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