The incident occurred during the Hammers' damaging 5-2 loss at home to the Gunners last Saturday, which saw the east London side concede all five of their goals in the first half.
Tensions boiled over between Lopetegui and Todibo, who joined on loan from Nice with an option to buy for £35million in the summer, during the defeat.
The 24-year-old defender vented his frustrations to his manager at half time.
This led to a heated row between the pair.
Despite their clash, Todibo played the rest of the game, with no other senior central defenders on the bench.
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He missed West Ham's 3-1 defeat at Leicester on Tuesday night due to a persistent groin problem.
Lopetegui has already been involved in a disagreement with another West Ham player since becoming manager in the summer.
He fell out with Mohammed Kudus in the 1-1 draw at Brentford in September after dragging him off at half time.
Almost £130million was spent on new players over the summer after Lopetegui's arrival as David Moyes' successor.
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However, the former Wolves manager's position at the London Stadium is currently hanging by a thread.
West Ham sit 14th in the Premier League table, six points above the relegation zone with a goal difference of -9.
And talkSPORT understands West Ham are considering sacking Lopetegui due to their underwhelming start to the campaign.
The Hammers board are expected to hold crunch talks on Wednesday to discuss his future after their defeat at the King Power Stadium.
Sporting director Tim Steidten - who originally advised owner David Sullivan not to appoint Lopetegui - is understood to be pushing for a change.
talkSPORT previously reported Steidten has already held talks with ex-Borussia Dortmund boss and Edin Terzic, who has served on West Ham's coaching staff.
Ex-Denmark coach Kasper Hjulmand, has emerged as a surprise contender for the job.
Meanwhile, former Porto chief Sergio Conceicao and ex-Chelsea and Brighton boss Graham Potter are other potential replacements.
Lopetegui was named as Moyes' successor in May on a two-year deal, with the option for a third.
Speaking after the Leicester defeat on Tuesday, the Spaniard said: "It's a frustrating night as we deserved much more. Playing football is not easy.
"We had 31 shots in the opposition box, normally you have to win this match. We had many chances but did not score.
"Tomorrow, we will start looking for the next challenge, knowing we are able to change the situation.
"They want to win for them, for me and the club.
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"The next will be the most important, we must be focused."