If you have published it in a classical journal, you have passed the copyright to the publisher. Therefore, if you reuse such a graph, you do not only need to cite it, you also need to use the "get rights and permission" function the publisher provides and get a reusage license for your own graph. That is usually free of charge when it's for another journal article, but it has to be done.
The Rightslink license PDF then needs to be submitted along with the paper draft files, otherwise the editor may put the publication of your new paper on hold.
Since nowadays open access, often associated with a Creative Commons license, is more and more popular, the conditions here are softer because the copyright is not with the publishing company, but you still may be required to submit a Rightslink confirmation of that.
To me the question sounded like direct reusage of a graph and that's what my answer is about; in that case you need to use Rightslink. Replotting would indeed in most cases be sufficiently adressed by a self-citation and a "replotted from ref. []" note.
However, if the final graph has only a "mildly altered" appearance with respect to the original, you may be required to get a license with editing permissions, as well, depending on the license agreement you signed when publishing it. As I said, these reusage licenses are almost always free for usage in a journal publication, so just get one (takes two minutes once you know what you're doing) and noone can get you into trouble.
It sounds resonable what Jürgen Weippert said. But if I was you I would not just cut out the picture from the original article and implement it in my new one. Why don't you create a new one and slightly change it to fit your topic? I would also explain that this method was already used in another paper (because then it's just a method) and reference that paper.
Yeah, that's the whole point: not angering a lawyer and not getting put on hold by the editor in the publication process of your new article. Summarizing, the decision process is the following:
It's an exact reusage of the figure -> get copyright verification from Rightslink
It's the same figure design, but it's mildly edited -> get copyright+editing priviledge from Rightslink
The data points are replotted from scratch in a completely new figure -> no Rightslink required, but something like "replotted from ref. []"