A total of 104 players are taking part in the event in Berlin, which this year has the theme of "flight and friendship". They presented Merkel with a signed pink football on Thursday.
Players from Iran and Germany squared off in Wednesday's opening match, with further games scheduled to take place through Sunday between mixed teams made up of players from Sudan, Kenya, Libya, the Palestinian territories, Afghanistan, Libya, Greece, Italy and France.
Organiser Corinna Assmann, who co-founded Discover Football in 2009, said there would also be workshops on issues such as sexism, self-defence, power and privilege during the festival.
"For us sport is the second most important thing -- it's mainly about the exchange and meeting between players, sharing experiences and learning from each other," she said.
Parya Norouzi, 28, grew up in a soccer-mad family in Iran and has been playing the game since she was five years old.
"Not just football but every sport that you do gives you self-confidence and it's good for you mentally and physically," she said through an interpreter ahead of the visit to see Merkel.
(Reporting by Michelle Martin, Andrea Shalal and Erik Kirschbaum; Editing by Catherine Evans)
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