True (but with one caveat).
This picture, put out by the Obama administration, has been floating around the internet for awhile now. The fact, though, did not originate with the Obama administration but with Mark Sheilds, a PBS commentator back in 2012. The statement has actually been fact-checked before by PolitiFact.com, a project of the Tampa Bay Times, which compiled a list of total deaths from all American Wars, as well as deaths by gunfire from 1968 to 2011. Their sources include the Congressional Research Service, The Centers for Disease Control and Prevention, and the FBI (you can read that article here).
The conclusion: the statement is true but with one caveat. Approximately 1.2 million deaths have occurred in all American wars, as opposed to 1.4 million gun deaths. The one caveat is that the data includes suicides and accidental gun deaths which some may not consider “gun violence.” This is noteworthy because the original statement from Mark Sheilds used the term “gun fire” rather than “gun violence.” That language was changed for this picture and it’s fair to say that it makes the statement less honest.