Reviewers say yes, but the filmmakers are coy.
Some review snippets:
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)
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 and kind of odd phrasing. Edwards clearly considered referencing it...
... but in an interview with Scifinow UK published May 16, he 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."
Here it sounds like pains were taken to avoid any reference.
I tend to believe that with all this consideration going on, whether the Janjira scene was inspired by Fukushima or not, Edwards is very conscious of what it evokes. In that sense, I would call it a reference, albeit one that for the moment he refuses to own.
According to Wikipedia, writing began in October 2010, five months before the March 11, 2011 earthquake and tsunami that compromised Fukushima. Rewrites continued through 2013. It's unclear when the scene was conceived or who conceived it, but a clue may lie in this Frank Darabont interview on io9 from January 2013:
Are you looking to connect it to a different contemporary issue [than the atomic bomb]?
Frank Darabont: Yes I am, but I'm not going to give it away.
This statement certainly could be about Fukushima/Janjira.
Caveats, other notes:
Imagery of a collapsed nuclear plant are evocative of feelings about Fukushima, but it's important to note that no such collapse occurred: the Fukushima disaster was due to flooding from a tsunami which compromised the plant's cooling system. The way crumbling U.S. buildings tend to evoke memories of 9/11, anything relating to Japanese nuclear safety may superficially be connected to the meltdown, but as of right now, what seems plainly evident is a false equivalency driven by emotion and distorted memories.
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 greater discussion about the Janjira scene once the country has a chance to react, and that reaction may dictate whether Edwards, Darabont or the other filmmakers feel comfortable explicitly stating the extent of influence that Fukushima had on the film. I'll try to keep this answer updated.