A ministry statement said the man arrested in Britain was a Salafist imam who led the group and who was sought by several countries. The 44-year-old imam was detained in the city of Birmingham at Spain's request.
The four arrests in Spain occurred in Mallorca, where the cell was allegedly based. The person arrested in Germany maintained contact with the cell and helped make propaganda videos. No names or nationalities of the six were released.
Around the same time, the imam was said to have visited the Spanish island of Mallorca to begin organizing the cell and to become its spiritual leader.
It said the imam was known by European police to have been recruiting militants and seeking finance for IS but that security measures he took and constant changes in address made his arrest difficult.
The ministry said the cell held regular meetings to recruit new members and actively promoted IS armed activities on social media. It said its increasing radicalization and willingness to commit jihad attacks led police in the three countries to make the arrests.