The answer provided by Marcus Adams is correct in the numbers, but I wanted to provide a bit more curated history and (hopefully) clarity.
TL;DR
I believe the 1000 character limit originally comes from RFC #821, not RFC #822. And it only enters the specification of Internet Message Formats in RFC #2822.
Network Message Formats vs Simple Mail Transfer Protocol
Just to make sure we are on the same page with terminology and stacks, I wanted to call out the differences here.
Network Message Formats
RFC #822 has a long history, starting at RFC #733 (1977) -> RFC #822 (1982) -> RFC #2822 (2001) -> RFC #5322 (2008) -> RFC #6854 (2013). With updates and extensions all over, like RFC #4021, RFC #5335 and RFC #5336.
All of these refer to the "message format" for "network messages" (aka email), with titles referring to "ARPA NETWORK TEXT MESSAGES", "ARPA INTERNET TEXT MESSAGES", "Internet Message Format", "Mail and MIME Header Fields", and more.
Simple Mail Transfer Protocol
However, there is also Simple Mail Transfer Protocol (SMTP) itself, which describes how to move (relay, transfer, etc...) email around the internet. It is defined in RFC #821 (1982). I bring up SMTP because this where we first see the size limits:
SMTP Size Limits
4.5.3. SIZES There are several objects that have required minimum maximum sizes.
* Note, the following are summaries, not a direct quote
user - 64 characters
domain - 64 characters
path - 256 characters
command line - 512 characters (including <CRLF>)
reply line - 512 characters (including <CRLF>)
text line - 1000 characters (including <CRLF>)
recipients buffer - 100 recipients
With an interesting note for the curious:
TO THE MAXIMUM EXTENT POSSIBLE, IMPLEMENTATION TECHNIQUES WHICH IMPOSE NO LIMITS ON THE LENGTH OF THESE OBJECTS SHOULD BE USED.
However, no limits in "Message Format" RFCs
First, RFC #822 does not specify any restraints on the length of the line, that I can see.
It does offer some guidelines for readability, but goes so far as to say,
3.4.8. FOLDING LONG HEADER FIELDS however, the limit is not imposed by this standard.
So I also looked at RFC #733 (which RFC #822 obsoletes) and this too recommends, but does not impose:
[Section III B.g]
The former length is recommended as a limit, but it is not imposed by this standard
However, although the referenced answer/comments point to RFC #5322 as imposing limits, it was actually RFC #2822 that introduced it finally. Again (the answer isn't wrong, just providing a path to it here).
So what does SMTP have to do with message format size limits?
According to RFC #822, in
1.2. COMMUNICATION FRAMEWORK
Messages consist of lines of text
And further, in
3.4.8. FOLDING LONG HEADER FIELDS
Each header field may be represented on exactly one line consisting
of the name of the field and its body, and terminated by a CRLF; this
is what the parser sees.
We can start connecting line length limitations headers to SMTP.
Ignoring folding, which does not change what a line means (just how to display it), RFC #822 explains that messages are just lines of text, and a header must be on exactly one line. But we need to go to RFC #821 to see the maximum line length is 1000 characters.
I hope first that I am correct on this, and only then, it provides some clarity.