It's still early days for Miitomo; the first app from Nintendo and DeNA has a long way to go before it will have firmly established itself. Nevertheless it enjoyed a positive launch in Japan and has since attracted plenty of attention in the West.
Since its 31st March release in territories such as the US, UK and Germany, the app has shown strong momentum. Though it's performing well on both iOS and Android it's on the Apple platforms where it's done best. Five days since launch (at the time of writing) it's still the number one free app on iPhone in countries such as the US and UK, and is top five in Germany.
Also notable is that, according to App Annie, the app has even grossed a reasonable amount in its early days in the US. At the time of writing Miitomo is among the leading 100 top grossing (87th at present) apps in the US; considering it's free-to-start with rather limited and modest monetisation that seems reasonable. Evidently a number of users are paying real money for in-game coins.
Similar Web has also been weighing in on early statistics, showing that on average Miitomo is demonstrating impressive levels of engagement per user. Taking statistics from the more established Japanese release, it states that many are keeping the app and using it regularly (it's too soon to pay much attention to Western figures in these areas).
Japanese app users have taken to the app almost immediately, and as of April 2nd, 3% of all Japanese Android devices had Miitomo installed on them. Since its release, these users have been spending an average of over 22 minutes a day on the app, and have made it the 13th most popular social app in Japan. Furthermore, our recent Uninstalls Report showed that many apps lose their users within the first 3 to 7 days, which does not seem to be the case with Miitomo, as the app is showing an above average retention rate early on.
Overall Nintendo and DeNA's first app seems to have enjoyed a solid start. It'll be interesting to see how it progresses, and also what the companies being to smart devices next.