Solana's warning was the EU's highest-level intervention to date regarding the polls.
It follows an EU report in November noting uneven progress in reforms to ensure democracy and the rule of law.
The report also said that the government was failing to tackle corruption in Albania, one of Europe's poorest countries.
While Brussels says all the countries of the western Balkans, including Albania, may one day join the EU, they face a long wait as many Western Europeans fear that the now 27-member club may have overstretched itself.
Albania took a first step towards membership in June when it signed a stabilisation and association agreement, but it is not considered ready for further progress towards candidate status.
The current dispute began months ago when the opposition Socialist party demanded a postponement of local polls to resolve disputes over voter lists and other areas where it believes that it may be disadvantaged or cheated outright.
Berisha had refused to delay the vote from January 20, but he gave in to the opposition's demands this week.
The new date still requires presidential approval, but this should be a formality.
Democratic party members say the Socialists fear a meltdown at the polls because they are badly divided and the party leader's, Edi Rama, who took over from veteran Fatos Nano in 2005, is weak.
Albania's two dominant parties in the post-communist era, the Socialists and the Democrats, have contested every election bitterly since 1991, in campaigns featuring unsparing rhetoric and often climaxing with refusals to accept results.
Solana called on the government and opposition to work to ensure an orderly vote. "I also look forward to the full and active participation of all political forces in the local elections themselves," he said.