Quick version: it looks that way, but the filmmakers are being very coy.
In an interview with the NY Daily News published May 11, 2014, director Gareth Edwards says:
“As we were writing the film, the horrible events in Fukushima happened and we had to make the decision: Do we stay away from that or do we acknowledge that you’ve opened this Pandora’s box of nuclear power, and when it goes wrong, it really does go wrong?”
This is careful phrasing. Edwards doesn't confirm that the scene is inspired by the Fukushima Daiichi nuclear disaster, but acknowledges that some sort of reference was on the table for discussion. He considered incorporating it into the film. This may be that.
In an interview with Scifi UK published May 16, Edwards says:
“When you list what makes a Godzilla movie two of those things that come up are radiation and Japan, and so once the events happened that were horrific for real in Japan, we had to be very careful and sensitive not to do something that would be considered insensitive to what happened there.
“Our film is not based on anything to do with Fukushima, it’s in a fictional city outside of Tokyo and happens 15 years ago, but that said it does deal with the genuine problem of around the world we have these nuclear power plants and we benefit from it."
This again is careful phrasing. The implication is that they made a conscious decision to carefully incorporate Fukushima into the film somehow. Of course the film is not about any real-world event.
According to Wikipedia, scriptwriting began in 2010, before the March 11, 2011 earthquake and tsunami that compromised Fukushima. Rewrites continued through 2013. It's unclear when the nuclear plant scene was conceived or who helmed it into rewrites, but evidence points to Frank Darabont who said said in an [interview with io9] in January 2013:
Are you looking to connect it to a different contemporary issue?
Frank Darabont: Yes I am, but I'm not going to give it away.
It certainly seems like a reference.
Reviewers are quick to make the connection:
Godzilla's basic plot centers around the fallout, literal and metaphorical, from a Fukushima-like nuclear plant meltdown. (Ars Technica)
[Janjira is] a barely-disguised reference to the real-world Fukushima nuclear plant meltdown... (Times of India)
The movie opens with a disaster at a Japanese nuclear power reactor -- an obvious reference to the 2011 incident at the Fukushima facility. (HuffPo)
Imagery of a collapsing nuclear plant are evocative of what we feel Fukushima was like (though no such collapse occurred; the meltdown was due to flooding from the tsunami caused by the 3/11 earthquake which compromised the cooling system). The way collapsing buildings tend to evoke memories of 9/11 regardless of context, anything relating to Japanese nuclear safety is likely to be compared to the meltdown.
Disclaimer: As of this writing Godzilla (2014) has only been in theaters for about a week and is not yet released in Japan. I expect a great deal of discussion on the topic once the whole world has a chance to react to and digest the film, and perhaps then the filmmakers will feel comfortable explicitly sharing their inspirations. Maybe in the DVD commentary, maybe much sooner! I'll try to keep this answer updated.