It has been reported the German Football Association (DFB) is considering disciplinary action against Sancho, as well as a couple of others, for a technical breach of the game's laws.
Under Law 4 Section 5, players are not supposed to have slogans, statements or images on their kit or other equipment which could be deemed as political.
However, FIFA has urged governing bodies applying those laws to "use common sense and have in consideration the context surrounding the events".
Infantino said: "For the avoidance of doubt, in a FIFA competition the recent demonstrations of players in Bundesliga matches would deserve an applause and not a punishment.
"We all must say no to racism and any form of discrimination. We all must say no to violence. Any form of violence."
"Where any behaviours or gestures on the pitch that may constitute a breach of the Laws of the Game have to be assessed, they would be reviewed on a case by case basis with a common sense approach and understanding of their context.
"The power of football can break down barriers across communities and we remain deeply committed to removing all forms of discrimination from across the game we all love."
It is understood that taking the knee in the manner in which Borussia Monchengladbach forward Marcus Thuram did would be unlikely to attract any sort of sanction.
But taking the knee in a way which could be viewed as provocative, perhaps doing so deliberately in front of someone who has previously been charged with or found guilty of a racism-related offence, may warrant further action.
Human rights group Amnesty International says it would "applaud" any athlete making a gesture of solidarity on this matter, including opting against competing in the US.
Its UK director Kate Allen said: "Numerous British sporting figures already speak out about racism and other human rights issues here in the UK, so it's likely some will be moved to say something about the appalling scenes in the USA.
"As we saw with Liverpool football players this week, taking a knee is just one of the many things sporting figures can do if they want to express their anger at US police violence against people of colour.
"Whether UK athletes go to the United States – or anywhere else – will always be a matter for them, but from black power salutes in the sixties through to Colin Kaepernick's famous gesture in 2016, sporting stars have shown they can make important human rights interventions."
"Every American needs to ask themselves, is there 'liberty and justice for all' and if their answer is yes, then they are part of the problem. In no way are we asking black lives to matter more than white lives," he wrote.
"All we're asking is we are seen as equal, as more than 3/5 of a man, as humans. My heart goes out in solidarity to George Floyd, his family, and all of the countless number of victims that have had their lives taken at the hands of meaningless police brutality."
Floyd Mayweather's promotion company confirmed the former five-division world boxing champion has offered to pay for George Floyd's funeral expenses.