I did a search on the Internet and didn't find anything about a shortage of IVIG.
On the supply side, I saw that the Plasma Protein Therapeutics Association (PPTA), an international organization with offices in Asia, Europe and the USA, had issued a statement (on February 17, 2020, as updated) stating that the coronavirus is not a concern for the safety of plasma protein therapies, including IVIG, manufactured by PPTA member companies, in large measure because "donor screening procedures are in place to prevent individuals from donating plasma who show typical disease symptoms (raised temperature/ fever, cough, difficulty breathing) of a coronavirus infection, including COVID-19. The SARS-CoV-2 is a large sized virus (approximately 120 nm in diameter). The relatively large size and lipid envelope makes it highly susceptible to steps with virus inactivation and removal capacity used during the manufacturing processes, such as solvent-detergent (S/D), low pH incubation, caprylate-, pasteurization- or dry-heat treatments, nanofiltration or fractionation processes and others. The effectiveness of these processes has been demonstrated on other lipid-enveloped model viruses which are quite similar to 2019-nCoV, e.g. human coronavirus 229E and OC43, SARS-CoV, and porcine coronavirus TGEV" see https://www.pptaglobal.org/media-and-information/ppta-statements/1055-2019-novel-coronavirus-2019-ncov-and-plasma-protein-therapies
On the demand side, however, I see that there is a recent (February 24) WHO report on the virus and it makes mention, on page 37, that in the clinical management of severe and critically ill coronavirus patients, the effectiveness of additional investigational treatment options, including IVIG, is an option that physicians may want to try, see https://www.who.int/docs/default-source/coronaviruse/who-china-joint-mission-on-covid-19-final-report.pdf Obviously, this is a potential concern for the rest of us users.