Bryan Garner, Garner's Modern American Usage, second edition (2003) has a useful entry on this matter:
DATES. ... B. Month and Year. February 2003 is better than February of 2003. Stylebooks have long agreed that no comma should appear between the month and the year. Among the mountains of evidence that might be amassed are these sources: The Washington Post Deskbook on Style 127 (1978); Kate L. Turabian, A Manual for Writers of Term Papers, Theses, and Dissertations 30 (5th ed. 1987); Publication Manual of the American Psychological Association 63 (4th ed., 1994); Scientific Style and Format 227 (6th ed., 1994); Joseph Gibaldi, MLA Handbook for Writers of Research Papers 70 (1999); Allan M. Siegel & William G. Connolly, The New York Times Manual of Style and Usage 101 (1999); Webster's New World English Grammar Handbook 161 (2001); The Chicago Manual of Style 253 (15th ed., 2003).
It is therefore strange to encounter an article in The New Yorker, one of our best-edited journals, in which January, 2000 and March, 2000 appear on the first page, and then five similar references appear throughout the piece. (See Scott Turow, "To Kill or Not to Kill," New Yorker, 6 Jan. 2003, at 40–47.) This seems anomalous: almost every professional editor would immediately delete the superfluous commas.
Garner might also have mentioned The Associated Press Stylebook and Briefing on Media Law (2002):
When a phrase lists only a month and a year, do not separate the year with commas. When a phrase refers to a month, day and year, set off the year with commas.
EXAMPLES: January 1972 was a cold month. ...
and Words into Type, third edition (1974):
When only the month and the year are given, commas are unnecessary.
[Example:] He began writing in May 1971 and finished in April 1972.
and The Oxford Guide to Style (2002):
7.10.1 Order [in Dates] Dates should be shown in the order day, month, year, without internal punctuation, as 2 November 1993. A named day preceding a data is separated by a comma: Tuesday, 2 November 1993. There is no comma between month and year: in June 1831.
On the other hand, a quick check of the December 11, 2017 issue of The New Yorker finds the magazine still hewing to the practice of including a comma in "month year" phrases. For instance, Jon Lee Anderson, "Accelerating Revolution,"uses it six times:
The battle, fought by Bolívar's partisan's and Spanish royalists in June, 1821, was the crucial victory ... In February, 1992, Chávez launched a coup attempt ... In December, 1993, Maduro went with a group of young comrades ... In legislative elections in December, 2015, the opposition trounced the P.S.U.V., ... In November, 2016, Maduro said, ... He was alluding to an executive order that Obama had signed in March, 2015 ...
As with all issues involving punctuation style, the first question a writer should ask in, "What style guidelines am I obliged to satisfy?" If the answer is "None," the writer can decide whether to follow preponderant publishing-house usage or to follow personal preference (if the two do not coincide). And in the case of "month[,] year" punctuation, the preponderance of usage clearly supports the no-comma option.