I don't know the exact number, but we do know some of them already:
Egypt, from the screenshot (Borders).
Japan, from the screenshot (Samurai).
England, from the screenshot (Ship of the Line, so I've been told).
I've also seen in an article someone talking about some Civs being in the game:
Greece
Aztecs
From there we can make a few educated guesses as to which other Civs will appear.
First are the obvious ones and the series staples:
America
China
Russia
France
Germany
India
Rome
Persia
That's 13 Civs we either know are in the game, or we can safely assume are going to be. Now, Civ 5 had 18 Civs at launch, so if we assume that number will be more or less the same we can guess at a few other Civs they might want to add.
An African Civ (Zulu, Songhai, South Africa, et cetera).
A native North American Civ (Iroquois, Sioux, et cetera).
A Central American Civ (Mexico, Maya, et cetera).
A colonial South American Civ (Brazil, Argentina, Columbia, et cetera).
An/another Middle Eastern Civ (Arabia, Babylon, Ottomans, et cetera).
Another Mainland east Asian Civ (Siam, Mongolia, Korea, et cetera).
An Australian Civ (Australia or Aboriginal Australian).
Joking aside, as much as I'd like Canada in Civ6, it probably won't happen in the base game.