Where is the smallest park by area?

I nominate Tjoffsans Tivoli in Malmö, Sweden. It is an amusement park for mice (also known as amousement park) created by Anonymouse MMX. It's not owned by any government, but it's public and maybe it could be classified as a charity.

It looks like it covers an area of approximately 1-2 m². It's unclear whether it is still open though.

The other answers show non-official parks or "novelty" parks that you cannot actually fit a person into.

Hence, I nominate Jack Early Park, San Francisco, CA. It has a flight of stairs leading up to a concrete platform with two benches. You get a nice view over the bay.

I could not find any data on its size, but from having been there myself I estimate the area to not be much more than 25 m² (only counting the platform, not the stairs).

It is hard to find a good picture of the whole park, since it is a small platform. I recommend viewing the 360° view on Google.

(c) 2009 Bryan Costales

Of course, in Japan everything is smaller. This one is 0.25 square metres, complete with bench. However, it's not technically a park, but a road feature, so it doesn't qualify for the Guinness Book of Records:

See Japanese Wikipedia or a local web page for more details.

While not the smallest park in the world, the smallest park in the UK is Prince's Park in Burntwood, Staffordshire.

Photo © Geoff Pick via Wikipedia Commons, CC-BY-SA

Google Street View link

It was built in 1863 to commemorate the marriage of the future king Edward VII, and in 2013 was the location for the UK's shortest fun run, with the slowest competitor finishing in a mere 55 seconds: link.

I nominate the small corner lot at North Pacific Avenue and Mission Street, Santa Cruz, California. I concede it is not named as a "Park," and doesn't appear in the City's list of parks, but it is treated as a park by the City and its residents, and is maintained by the City.

Here's a Street View Picture. The public area is between the blue wall and the street from which the photo was taken:

I bet that the Heemskerk Lunet 10 does make a good chance as the smallest 'national park like' park, as it is a rather small bit of ground owned by Noordhollands Landschap.
Here is a link to it on google maps.
And here is a link to the charity that manages it as well as several others in the area.

I can not find any official information, the charity does not give it on their site. Google maps gives me about 100 x 82 meter, which would give me 8200 m², but that is not very precise.