Edinburgh's Dickinson, 32, lasted only a couple of minutes as the Scots opened their two-Test series with victory.
"We'll have to have a look at Al Dickinson," Cotter told BBC Scotland.
"Bit of a concern and we'll be looking at alternatives. If he can't take the field next week, we'll look at bringing somebody over."
Cotter is hopeful other knocks picked up at the Toyota Stadium can be managed before next Saturday's match in Tokyo.
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"Huw Jones should be okay [to provide cover in the backs]," said the New Zealander. "Hopefully we'll be able to fill the absence of Duncan Taylor [at centre] if he can't play with what we've got.
"WP Nel was a little bit sore coming off, also. [We'll have] a full assessment, see if these guys can be back at 100% and we may have to rotate the team a bit."
Nel scored Scotland's second try in Toyota City after a penalty try had put the Scots in command before the break. There would be no further scores, with Shota Horie crossing for Japan early in the match.
When Nel went over early in the second half, Japan were down to 13 men with Hendrik Tui and Rikiya Matsuda yellow-carded, the latter's knock-on giving the Scots their penalty try.
"First of all, I'm happy - the win is what we were after," said Cotter.
"The way we got it was probably done in a complicated fashion. We gave the ball back to them a number of times and had to work our defence. We did work our defence and I thought we defended reasonably well.
"Our set piece held up without being great but it was still holding up and gave us a platform.
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"I thought our discipline was key. They gave away a couple of yellow cards, a penalty try and it was the pressure we put on them by getting down in there into the paddock. We managed to get, I think, 19 turnovers off them.
"The boys aren't particularly happy and next week we know Japan will lift their game. We'll have to lift ours."
Greig Laidlaw's 16 points with the boot came from six kicks out of six and the captain said: "We were pleased to win and we probably need to just tighten up a little more and be a little bit more accurate.
"At times in the second half we just gave the ball away and maybe let Japan off the hook."
Scotland head coach Vern Cotter may call up a replacement for Alasdair Dickinson after the prop came off injured in the 26-13 win over Japan.