No.  The IRS has no special reporting requirements for organizations that temporarily suspend their operations.  There is a question 3 in Section III of the annual Form 990 about whether the organization ceased conducting or made any significant changes in how it conducts, any program services.  It doesn’t ask about “suspension” of services.  If you should answer “yes” to the question for any reason, it will go on the Form covering this part of 2020, not on the Form coming due for calendar 2019.  (The IRS has just extended the date for filings that were due on May 15 for the 2019 calendar year until July 15, 2020.)

Just be sure that you file a Form 990, 990EZ, or 990N for each year, whichever type is applicable, including 2019.  An exempt organization (including exempt organizations other than 501(c)(3)) that fails to file some version of a required Form 990 for three consecutive years will automatically lose its exemption.  The exemption can usually be recovered, but that is a real pain.