2018 MLB Roster by birth countries
There were 1,533 total players that appeared in 2018 regular season (*There are duplicates, because traded players will show up multiple times) and they are born in 26 different countries and territories. Here is the breakdown of those players by country of birth according to baseball-reference:
1,100 are from 
United States,
158 from 
Dominican Republic,
117 
Venezuela,
30 
Cuba,
28 
Puerto Rico,
23 
Mexico,
12 
Canada,
9 
Japan,
8 
South Korea,
7 
Colombia,
6 
Curacao,
6 
Panama,
4 
Brazil,
4 
Germany,
4 
Netherlands,
4 
Taiwan,
3 
Australia,
2 
U. S. Virgin Islands,
1 
Aruba,
1 
United Kingdom,
1 
Guam,
1 
Hong Kong,
1 
Lithuania,
1 
Nicaragua,
1 
Saudi Arabia, and
1 
South Africa.
Source: Baseball-Reference.com's team page, Full-Season Roster & Games by Position table
Single JSON file of 2018 MLB pLayers list in gist. * since it is a roster of each team, traded player appears multiple times, i.e. Manny Machado appears in BAL and LAD.
Flags are originally from Flagpedia but edited to 40w x 20h uniform size
More breakdowns (sums)
Players
United States 1,100
Dominican Republic 158
Venezuela 117
Cuba 30
Puerto Rico 28
Mexico 23
Canada 12
Japan 9
South Korea 8
Colombia 7
Curacao 6
Panama 6
Brazil 4
Germany 4
Netherlands 4
Taiwan 4
Australia 3
U. S. Virgin Islands 2
Aruba 1
United Kingdom 1
Guam 1
Hong Kong 1
Lithuania 1
Nicaragua 1
Saudi Arabia 1
South Africa 1
Games
United States 48,230
Dominican Republic 7,869
Venezuela 7,629
Cuba 1,957
Puerto Rico 1,844
Curacao 650
Mexico 613
Canada 493
South Korea 339
Japan 338
Colombia 313
Germany 296
Panama 198
Brazil 162
Aruba 136
Netherlands 134
Australia 95
Taiwan 70
Saudi Arabia 59
Nicaragua 51
Hong Kong 33
U. S. Virgin Islands 33
Lithuania 25
South Africa 13
Guam 7
United Kingdom 3
WAR
United States 698.6
Dominican Republic 91.6
Venezuela 87.1
Puerto Rico 28.5
Cuba 26.3
Curacao 14
Canada 10.8
South Korea 8.6
Mexico 7.9
Japan 6.4
Panama 6.2
Netherlands 4.2
Aruba 3.8
Germany 3.5
Colombia 3.4
Brazil 1.6
Saudi Arabia 1.2
Australia 0.5
Guam -0.1
United Kingdom -0.2
South Africa -0.3
Hong Kong -0.5
Taiwan -0.7
Lithuania -0.9
U. S. Virgin Islands -0.9
Nicaragua -1.4