Ramires was sent off for a second bookable offence five minute from time against Bayern in Prague for a late challenge with studs on Gotze.
The German international has since been ruled out for a few weeks with an ankle injury sustained in the tackle, missing international duty as a result.
Dante has insisted that Ramires did not mean to injure his colleague and wanted to send an apology to Gotze for the tackle.
He told Bild: "Ramires is an incredibly kind person and he's told me that he is very sorry about Mario's injury.
"He definitely did not want to injure him and he has asked me to apologise to Mario on his behalf. Mario's very important and he will come back stronger than ever."
Both Brazilians are currently on international duty with the Selecao ahead of a friendly against Portugal in Boston later tonight.