This is not to suggest that everyone should stay away from cats; it is a reminder to protect your own cat(s) and avoid letting them go outside whenever possible. So far, there is no direct evidence that cats transmit COVID-19, so please remain rational.
From two reports—one from an article by Shi Zhengli, see here. Note that the article does not say cats become infected; it only says that neutralizing antibodies for COVID-19 virus (SARS-COV-2) were detected in cats, and cats from owners who tested positive for COVID-19 had higher antibody titers. Of the sampled 143 Wuhan cats, about 15 were antibody-positive (note: most were weakly positive), and 11 had neutralizing titers only; there were no cat deaths reported. But cats owned by infected owners had especially high antibody titers, which indicates the virus has indeed activated cats’ immune systems in some cases.
Another report, from BBC, says that a tiger at New York's Bronx Zoo tested positive for COVID-19 viral nucleic acid after showing suspected symptoms such as a dry cough. A zoo keeper had already been diagnosed a while ago, so the infection is likely from that keeper. The tiger is currently in relatively good health.
For friends who have cats or tigers at home, protect them and keep them from going out as much as possible. Also, there have been reports that dogs may also be infected, and there have not yet been reports or direct evidence of pet-to-pet or pet-to-human transmission. In any case, keep your cats and dogs at home from unnecessary outings for now, especially in crowded places.