The Mexican government has promised to make vaccinations available free of charge across the country of almost 129 million people -- a massive logistical challenge -- starting with frontline health workers.
Ahead of the virtual visit, Guterres said he was honoured to "renew our cause of overcoming global challenges together, and celebrate a country that was instrumental in creating the United Nations".
Those figures put the government far short of its goal of vaccinating 20 million people by the end of 2020, although officials said they expected the rollout would pick up significantly this month.
The benchmark Nikkei 225 index, which jumped 16 percent last year, lost 0.68 percent, or 185.79 points, to 27,258.38, while the broader Topix index was down 0.56 percent, or 10.09 points, to 1,794.59.
MSCI's broadest index of Asia-Pacific shares outside Japan hit a record high on hopes that the rollout of coronavirus vaccines will eventually help revive the global economy.
The US Federal Reserve is expected to keep interest rates pinned near zero and to signal where rates are headed in the coming years at it's final policy meet of the year. The Fed's policy statement is due at 1900 GMT.